{'fraction_non_alphanumeric': 0.023679213671395062, 'fraction_numerical': 0.015134591756952977, 'mean_word_length': 4.939137645107794, 'pattern_counts': {'":': 0, '<': 14, '<?xml version=': 0, '>': 8, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high energy RS-II Braneworld

The swampland conjectures from string theory have had some really interesting implications on cosmology, in particular on inflationary models. Some models of inflation have been shown to be incompatible with these criterion while some have been shown to be severely fine tuned, with most of these problems arising in single field inflationary models in a General relativistic cosmology. Recent works have although optimistically shown that single field models in more general cosmologies can be consistent with these conjectures and hence there is an optimism that not all such models lie in the swampland. However a paradigm of inflation which has been shown to not be perfectly okay with the conjectures is eternal inflation. So in this work, we discuss Tachyonic inflation in the high energy RS-II Braneworld scenario in the context of the swampland conjectures while also considering the possibility of swampland consistent eternal inflation. We show that our concerned regime evades all the prominent swampland issues for single field inflation being virtually unscathed. After this, we show that the main conflicts of eternal inflation with the swampland can easily be resolved in the considered tachyonic scenario and in particular, we also discuss the exciting prospect of a Generalized Uncertainty Principle facilitating the notion of Swampland consistent eternal inflation. Our work as a whole reignites the possibility that there can be a swampland (and possibly, quantum gravitationally) consistent picture of a"Multiverse".


Introduction
The idea of Cosmic Inflation has achieved a tremendous amount of success in describing various properties of the early universe. [1][2][3][4][5] Numerous predictions of Inflation for the early universe have been repeatedly validated by various satellite experiments, and the most recent data from the Planck experiment follows this trend. [6][7][8][9] Further the observational data supports a huge variety of Inflationary models which are motivated from vastly different backgrounds, from Modified gravity theories to quantum gravitational realizations. [10][11][12][13][14][15][16][17][18][19][20] Inflation has not only been thoroughly studied in regimes where the inflaton is a scalar or a vector field, but also for very non standard scenarios as well where the Inflaton is a complex scalar, a tensor or even a tachyonic field  . A form of Inflation which has attained widespread interest in the cosmological community in recent decades is Eternal inflation. [47][48][49][50][51][52][53][54][55][56][57][58] Perhaps the most starkling outcome of Inflation continuing eternally is the production of a "Multiverse", as Inflation does not have to stop everywhere at once and can keep on happening in some parts of space while it ceases in some other parts.
There has been a lot of work dedicated towards a " Theory of Everything " in recent years, and arguably the most well known candidate for such a paradigm is String Theory. [59][60][61][62][63][64][65][66][67] As String theory presents itself in such a vivid mannerism, one can reasonably expect this theory to have wide ranging implications for cosmology. Consequently, there is a rich and diverse amount of literature which has explored the cosmological implications of the ideas of String theory. [68][69][70][71][72][73][74][75] Amongst the many cosmologically intriguing features of string theory is the incredibly high amount of possible vacua states it allows, which goes as high as O(10 500 ) and this goes to constitute what is known as the "landscape" of string theory. A natural question which then arises is exactly what class of low energy effective field theories are actually consistent with String theory. In a bid to answer this question, Vafa introduced the term "Swampland" to refer to the class of low energy effective field theories which are inconsistent with the framework of String theory. 76 Further, in recent years a number of field theoretic UV completion criterion from string theory called the "swampland conjectures " have been proposed [77][78][79][80][81] which classify whether a given regime lies in the swampland or not. As string theory is also seen by many as a viable paradigm of quantum gravity, if a low energy EFT satisfies these criterion then it could also potentially be on amicable terms with a self-consistent theory of quantum gravity. While there have been a considerable number of swampland conjectures (and their modifications) proposed in recent times, the conjectures which have had very telling cosmological implications are : 1 : Swampland Distance conjecture (SDC) : This conjecture limits the field space of validity of any effective field theory 78 . This sets a maximum range traversable by the scalar fields in an EFT as where c is some constant of O(1) , and V is the scalar Field Potential. Another refined form of the Swampland De Sitter Conjecture (RSDSC) places constraints on the hessian of the scalar potential (a finding which first appeared in 79 and later in 85 ) and is given by These conjectures have pretty interesting implications on cosmology and in particular on single field inflation. It was shown in 86 that single field inflation in a GR based cosmology is not consistent with these conjectures, considering the data on Inflation. 6, 7 A lot of work has been done to alleviate this conflict. [87][88][89][90] It has ,however, been shown that if the background cosmology for single field inflation is not GR based then this regime of inflation can still be consistent with the swampland criterion. [91][92][93][94] Particularly, in 95 it was shown that (cold) single field inflation can be consistent with these criterion in a large class of non-GR based cosmologies. It's also worth noting that the paradigm of warm inflation 13 has also been shown to be quite consistent with the swampland criterion for single models in both GR and non-GR based cosmologies. [96][97][98][99][100][101][102] Another swampland conjecture which has gathered quite an immediate interest with regards to inflationary cosmology is the recently proposed "Trans Planckian Censorship Conjecture"(TCC). 81 It was shown in 103 that single field GR based inflationary models can only be consistent with the TCC if they are severely fine tuned, which is quite ironic considering that inflation was made to solve the fine tuning problem in standard big bang cosmology. A lot of work has further been done to understand the issues of the TCC with single field inflation. 91,[104][105][106][107][108][109] In, 110 it also shown that the TCC can actually be derived from the distance conjecture (1) considering that latter criterion is true. Single field models in non standard inflationary regimes have been shown to not be severely fine tuned due to the TCC, unlike their counterparts models in a GR based cosmology. 111,112 The current literature on inflation and the swampland criterion hence suggests that these conjectures support the notion that early universe expansion happened in a non standard inflationary regime, considering that inflation was the cause of the expansion (and also with the added consideration of only single field models, because multi field models have been shown to be on a very good standing with the conjectures in even the standard paradigm 113,114 ).
While it has been shown that some paradigms of inflation can be rescued from the swampland with different schemes, eternal inflation has been one peculiar inflationary regime which has not been fully consistent with all the swampland conjectures till now. The conflicts of eternal inflation and the swampland were first highlight by Matsui and Takahashi in, 115 where they showed that one of the core requirements for eternal inflation was in direct conflict with the dS conjecture (2). Dimopoulos then considered eternal inflation on steep potentials with a turning point atφ = 0 (where φ is the inflaton field) and found that these models of eternal inflation were also in conflict with the dS conjecture. It was then shown by Kinney 116 that eternal inflation can be consistent with the Refined dS conjecture (3), and this could prevent eternal inflation from being in the swampland( as it has been shown that consistency with either of (2) or (3), if not both, can prevent a paradigm from plunging into the swampland 79 ). But it was then shown by Brahma and Shandera in 117 that eternal inflation can actually not be consistent with the Refined dS conjecture as well. In addition to this, Wang et.al 118 showed that the Gibbons-Hawking entropy bounds for eternal inflation are also not consistent with the swampland conjectures , which is again a very serious issue for eternal inflation. Hence, it does look like eternal inflation has some unavoidable conflicts with the conjectures. However, a key point all of the ventures discussed above is that they considered eternal inflation in a GR based cosmology.The situation does look a tad bit better in more general cosmologies , as Lin et.al showed in 119 that certain hilltop models of eternal inflation in a braneworld cosmology can be consistent with the dS conjecture and its refined form. This is encouraging and could point towards the idea that in order for eternal inflation to be consistent with the swampland conjectures, one should look towards regimes which are motivated by String theory (as braneworld cosmology also has its roots in string theory [120][121][122].
A regime of inflation which was inspired from string theory itself is tachyonic inflation, 21 where the inflaton field is considered to be of tachyonic nature. This paradigm of inflation has been shown to be consistent with the swampland criterion in a GR based cosmology for a warm inflationary setup 28 under some conditions. Tachyonic inflation has also been studied in a braneworld background cosmology, 24, 29, 123 so it would be quite interesting to see if tachyonic inflation on the RS-II Brane is consistent with the conjectures, as these scenarios for single field cases have always been on relatively amicable terms with the conjectures as compared to GR based paradigms. Further, eternal inflation with tachyonic fields in the braneworld can present a great chance of being consistent with the conjectures and the reasons for that are two-fold. First, braneworld inflationary scenarios have proven to be a great fit with the swampland conjectures in a diverse range of regimes and this cosmological setup, as noted above, traces its roots in string theory itself. Secondly, tachyonic models of inflation are also inspired by string theoretic properties and hence, one can be optimistic in exploring the consistency of such a string influenced regime with the conjectures for eternal inflation. Indeed, in our paper we show that this is indeed the case and hence, this paper is structured as follows. In section II, we discuss some of the basic features of tachyonic inflation after which we show that tachyonic inflationary models in the high energy RS-II Braneworld are virtually unscathed by the swampland conjectures and are consistent with all of the criterion individually too. Then, in Section III we show that eternal inflation with tachyonic scalar fields in a braneworld scenario suffers no issues with the swampland conjectures and finally in Section IV, we conclude with some final remarks on our explorations.

Tachyonic Inflation in the RSII Braneworld and the swampland criterion
We start with the 4-dimensional action of the tachyon field minimally coupled to gravity, which can be written as 21, 23 The stress energy tensor in a spatially flat FLRW metric ds 2 = −dt 2 + a(t) 2 dx 2 is given by is the Lagrangian density of the Tachyon field , V (φ) is the potential, while ρ φ and p φ are the energy and pressure densities of the field given by The Friedmann equation for a Randall-Sundrum II Braneworld cosmological scenario is given by [ for details on this, please refer to [124][125][126][127] ] where we are working in c = = 1 units, with ρ being the energy density, λ being the brane tension , Λ 4 being the 5D cosmological constant and ω being the so called "dark radiation " term. As we are considering the very early universe, we can ignore the cosmological constant term, whereas the dark radiation term vanishes rapidly due to the a −4 dependence. So, we can write the friedmann equation during inflation as From the action, one can arrive at the field equation of motion as, 23 while one can also use energy conservation to write , In the slow roll limit of inflation with tachyonic scalar fields, we haveφ << 1 and φ << 3Hφ , which allows us to write the Friedmann equation and the field equation of motion as, it's immediately apparent that (12) reduces to the usual Friedmann equation for a GR based cosmology H 2 = V 3m 2 p in the low energy limit λ >> V . Hence, to better illustrate the effects of the braneworld scenario for inflation, one can instead consider the high energy limit of the picture V >> λ, which allows us to now write the Friedmann equation (12) as, The Number of e-folds can be written using it's usual definition for some initial field value φ i to some final value φ e as, And using the approximation (13), we can then write the e-fold number as Further, using the Friedmann equation (14), one can write N as A particularly important class of parameters for any inflationary model are the slow roll parameters 10 and in particular, the ǫ and η parameters. One can define these parameters for tachyonic brane inflation through their usual definitions in the high energy limit as , Further the power-spectrum of the curvature perturbation P R that is derived from the correlation of first order scalar field perturbation in the vacuum state can be written a as 29, 128 where in the slow roll limit, one can ignore the contribution ofφ. One can then further find out other observationally revelant perturbation parameters like the scalar and tensor spectral index, tensor-to-scalar ratio etc. using their standard definitions. 21, 23, 128 We will not illustrate that here as we have built enough groundwork to start seeing why tachyonic brane inflation is consistent with the swampland in the high energy regime. The prominent issues of conflict between the swampland conjectures and single field inflation which were discussed in length in 86 can be briefed as follows. One of the issues concerns the dS conjecture and inflationary requirement for the ǫ parameter, as it was shown that if one considers the dS conjecture seriously than the requirement that ǫ << 1 is categorically not satisfied. Another issue concerns the fatal constraints that the dS and distance conjecture applied together have for the e-fold number, as they constrain N << 1 which is quite clearly in violation of the bare minimum inflationary requirements on the number of e-folds.Finally, the third main issue which was elaborated in 86 is the inconsistency between constraints set on the η parameter from observational data on inflation 7 and the implications that the refined dS conjecture has on the same parameter.We will now elaborate under what conditions Tachyonic Inflation on the RS-II Braneworld evades all of a At this point it is important to clarify about the applicability of this form of the power spectrum in the model we have considered as one might think that the amplitude needs some corrections. Indeed there are corrections to the power spectrum amplitude when one considers non-GR based scenarios butthe form considered here has been shown to be an appropriate approximation in this regard. In the context of the RS-II braneworld scenario, Einstein Equation in 4D would be modified because of the effect of the extra dimension which might change the scalar perturbation part as well at the background level or Friedman equation. There are indeed modifications in the formula of scalar power spectrum because of the modified first Friedman Equation (12) which can be taken into account easily in (20) ( but we have not done so because the premise of our analysis did not require that). However, the effect of the modification of the perturbation equation is negligible, and with a good approximation, Eq. (20) is quite okay. It has been used previously for describing tachyonic inflation in the RS-II braneworld successfully, see for example 29 where the authors used the same form of the power spectrum to construct a viable tachyonic braneworld inflationary scenario.
the issues of single field inflation b with the swampland conjectures. Firstly, focusing on. The ǫ parameter (18), can be written as Considering the dS conjecture (2) in this scenario, we can write As c ∼ O(1) , in order for ǫ << 1 , one would require Hence, it would appear that the dS conjecture implies a constraint on the energy scale of inflation ( as during inflation ρ = ρ φ ≅ V ) for tachyonic inflation on the RS-II braneworld. But, it is far from the case as we recall that the formulation built above is in the high energy limit of the braneworld, which characterized by V >> λ. So in reality, tachyonic inflation in the high energy RS-II braneworld is not strongly constrained by the dS conjecture and is virtually unscathed. Similarly, the change in the e-fold number during inflation can be written using (17) as, Now considering both the distance (1) and dS conjecture , we see that term in the square brackets in (24) has to be less than unity. This shows that in order to have sufficient amount of e-folds, one again needs and once again as we are in the high energy limit already( V >> λ), the requirement (25) does not pose a very strong constraint on the energy scale of inflation in such a regime which might have otherwise ruled out some inflationary models in this scenario. So this makes it clear that there is no issue of a insufficient e-fold number for this inflationary regime. Finally we note that even if one considers both the dS conjecture and the refined dS conjecture (3) to simultaneously hold true and applies them the on η parameter (19), the observational requirement for η ≤ 0 is still identically satisfied as both terms in the square bracket in (19) become negative . In conclusion the only "constraint" applied by the swampland conjectures on tachyonic inflation in the high energy RS-II Braneworld is a small lower limit on the energy scale of inflation, which in the high energy limit is quite intrinsically satisfied.
b One could probably ask whether tachyonic branewrold models have any realism attached with it and we would like to address that here. Various inflationary regimes in the RS-II Braneworld with a tachyonic scalar have been shown to be observationally viable, with both cold and warm inflationary models being supported in this regard. Some works have been exclusively based on confronting such models with observations and have had positive results, see for example. 24,29,123 With this we see that this regime of inflation is strictly not in the swampland for effectively all kinds of potentials. As we have now demonstrated that our concerned inflationary paradigm is quite consistent with the swampland conjectures, we now proceed towards showing how eternal inflation in this regime is also consistent with these criterion.

Swampland consistent Eternal Inflation
As discussed in section I, recent works have shown that eternal inflation is not on an amicable standing with the swampland conjectures . One of the key requirements in order for eternal inflation to take place in any kind of regime that quantum fluctuations of the inflaton field should dominate over the classical field evolution.
The amplitude of quantum fluctuations on scales of order the Hubble length is given by (the following expression is independent of the underlying gravitational theory 23 ) while the classical field variation in Horizon time H −1 is given by The requirement that quantum fluctuations dominate the classical field evolution hence translates into In the usual case of single scalar field inflation, the criterion (28) transforms to the following requirement on the amplitude of curvature perturbations at horizon crossing The above requirement can eventually be shown to be inconsistent with the dS conjecture. 115,129 This was the first conflict highlighted between the swampland criterion and eternal inflation. It was then shown in 86 that the curvature perturbation amplitude requirement (29) can be amicable with the refined dS conjecture but it was further shown in 117 that the perturbation requirements cannot be consistent with the refined dS conjecture as well . Now writing the amplitude of curvature perturbations for tachyonic inflation (20) in the slow roll limitφ << 1, one gets From (30), it is immediately apparent that the condition (28) does not set a direct requirement on the amplitude of curvature perturbations for a tachyonic field like it does for a usual scalar field. Further for a large enough energy scale , just like the high energy limit of the RS-II Braneworld considered here, one can easily have P R (k) < 1 whilst still preserving the condition (28). Hence the conflicts of the swampland conjectures with eternal inflation in the presence of the requirement of P R (k) ≥ 1 [115][116][117] are not encountered for our concerned tachyonic regime.
Another very severe issue faced by eternal inflation is the inconsistency its entropy bounds have with the dS conjecture, something which was highlighted in 118 (we are not considering technical entropy based issues regarding stability and configurational problems as they lie beyond the score of our paper, as we are interested in the swampland issues here ). This issue is in particular focused for large field inflationary models and can be understood by considering the Bekenstein-Gibbons-Hawking entropy of the local event horizon of an expanding cosmology 130-132 During a period in stochastic inflation when the inflaton moves up the potential due to quantum fluctuations, H increases and thus the entropy of the area bounded by the horizon decreases. For the process above to be consistent with the second law of thermodynamics even after taking into account quantum gravitational effects, the variation of the entropy above is bounded as 133 Now if one considers a usual scalar field inflationary model based in a General Relativistic cosmology, then bound (31) eventually turns out to be in violation of the dS conjecture and thus leading to serious issue for the entropy bounds for eternal inflation which was discussed in. 118 This issue of entropy bounds, however, will not persist for Tachyonic inflation in a high energy RS-II braneworld which is what we now show. Using the Friedmann equation (14), one can write the variation of the entropy (31) as further, considering the change in entropy during a time in which using δφ = H 2π , we have Now, employing the criterion (32) leads to the following inequality The dS conjecture sets the limit mpV ′ V ≥ O(1), hence in order for the above inequality to be consistent with the dS conjecture we need November 10, 2022 2:36

ws-mpla
Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high energy RS-II Braneworld 11 Hence the dS conjecture sets a lower limit on the energy scale of tachyonic inflation in the high energy RS-II braneworld, for it to be on amicable terms with the entropy bounds. We note that the bound to bypass the entropy issue (36) is in the range with lower limit on the inflation energy scale (25) needed to evade the primary issues of the swampland and single field inflation discussed in Section II. So the crux of the matter here is that in order for the eternal inflation entropy bounds to be consistent with the dS conjecture in our concerned tachyonic regime, we need to set a higher lower bound on the energy scale of inflation which is still consistent with the bounds needed to sort out the primary inflationary issues with the swampland. There is, however, another way to go about the entropy bound issue. The event horizon entropy considered here is through the standard Bekenstein-Gibbons-Hawking entropy formulation, while in recent years there has been a lot of work which has explored corrections needed in (31) in order to accommodate the newly emerging physics from string theory and loop quantum gravity (LQG). [134][135][136][137][138][139][140][141][142][143][144][145] Several of these approaches have the quantum-corrected entropy-area relation in a general form in terms of (31) as where C n are parameters which are model dependent (like recent works have determined C o = − 1 2 for LQG 139 ). It was also interestingly pointed out in 146 that Heisenberg's Uncertainity principle might be affected by quantum gravitational effects. Since then, a significant amount of work has gone into finding a Generalized Uncertainty Principle(GUP) and we can discuss this work in short here. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. Furthermore, assuming modified dispersion relation allows for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker-Wigner inequalities, entropic nature of the gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. Another one predicts a maximum momentum and a minimal length uncertainty, simultaneously. One can consider a GUP of the form The above GUP is the generalization of the uncertainty principle which about from minimal length considerations and is known as the Kempf-Mangano-Mann (KMM) GUP. The KMM GUP can be deduced from following commutator where α can be either positive or negative. Its's important to stress though that the magnitude of α has been widely studied in the literature and has been seen to be positive mostly. For instance, in String theory it has been assumed to be of order unity. [147][148][149] From a straightforward analysis of the quantum corrections to the Newtonian potential, one can derive α = 82π 5 150 whereas by studying the deformed Unruh temperature in a maximal acceleration framework one would get α = 8π 2 9 . Similar results have been found in several wide ranging contexts in things like noncommutative Schwarzschild geometry 151 and even in the Corpuscular description of Black Holes. 152 While the KMM GUP is based on minimal length considerations, one can consider a different GUP of the form where β is again a parameter which can take on both positive and negative values. This GUP is due to Pedram 153,154 and has both minimal length and maximal momentum considerations. Again, the magnitude of β has been seen to not be of any extreme magnitudes in the literature. looking for the quantum corrections it provides to the usual Bekenstein-Gibbons-Hawking formulation of local event horizon entropy. This eventually led to the following form of the quantum corrected entropy due to a GUP, 138,140,143,144 where α o is dimensionless constant which is found in the deformed commutation relations and can be usually considered to be positive in nature. 145 The leading order contribution to the GUP corrected entropy formalism is due to the √ S BGH term, which is an extra term to the already existing logarithmic correction to entropy derived from the quantum gravity effects. Considering this form of entropy relation as the one for entropy of a local event horizon for an expanding cosmology has provided pretty interesting insights (see for example, 155 ). Hence, we now consider the form (38) of the entropy for the bound (32) and as we would like to entertain in particular the implications of the very interesting GUP effects , we only consider the leading order GUP correction to the entropy which provides us with which can be written in terms of the Hubble Parameter as Using the Friedmann equation (14), we can now write the entropy in terms of the potential This finally allows us to express the bound (32) in terms of the GUP corrected entropy as Rewriting the inequality above, we have The dS conjecture constraints , hence in order to maintain consistency with it the following inequality will have to hold The last inequality is a bit non-trivial but can be calculated using computing systems like Mathematica. This inequality sets a lower bounds on λ given by And also a lower bound on the inflation energy scale, which keeping in mind the brane tension bound can be written approximately as Hence the dS conjecture can be consistent with the GUP corrected eternal inflation entropy bounds given that the brane tension and the inflation energy scale abide by the above mentioned lower limits. The most interesting outcome of considering the GUP corrected entropy bounds is in the nature of limits implied in (45)(46). If these bounds are satisfied (these are in line with the basic requirements for the energy scale for consistency with the conjectures), then the famous issues which contribute to the failure of a swampland consistent eternal inflation picture are taken care of. Hence the direct relation between the inflaton energy scale and the constant α o which is found from the deformed commutation relations for a GUP is incredibly exciting. In this scenario, the existence of a Generalized Uncertainty Principle facilitates the creation of a swampland consistent eternal inflationary scenario and consequently, a swampland consistent multiverse. To make this peculiar relation even more clear, we would like to demonstrate that the consideration of a GUP corrected entropy formalism would also allow us to evade the dS conjecture-entropy bound conflict in a simple scalar field model in a GR based scenario. For GR based single field models , the Friedmann equation during the expansion phase is The GUP corrected entropy (39) for this regime becomes And hence, the bound (32) in this case takes the form It is worth mentioning the difference the GUP corrected has already made in eradicating the entropy bound issue for this inflationary regime. The above inequality clearly shows that it quite possible to satisfy the constraints due to the dS conjecture on the left hand side of the inequality, given that there is some minimum limit on the energy scale of inflation to make the right hand side of the inequality sufficiently large. Doing this would mean that the numerator on the right hand side far dominates over the denominator which using the Friedmann equation (47), can be written as the following inequality Hence one can eradicate the issue between the dS conjecture and entropy bounds by considering a GUP corrected entropy formalism by constraining the energy scale during inflation in accordance with the above bound for α o < 8 √ 3 . Once again, we notice how crucial a role the Generalized Uncertainty Principle based corrections make in allowing us to evade the entropy bound issues even in a usual scalar field model based in a GR based cosmology. This in no way shows that eternal inflation in such a regime is consistent with the swampland, however, as other issues regarding the conjectures still hold true. [115][116][117]129 But this does illustrate that GUP based quantum corrected entropy does facilitate positively in removing the entropy bound-dS conjecture conflict in multiple regimes of inflation. Thus we can draw a very exciting conclusion from this analysis that considering a generalized uncertainty principle makes it more easier for one to have a swampland consistent (and considering the premise of the conjectures, a quantum gravitationally consistent) picture of a multiverse generated by eternal inflation.

Concluding remarks and discussion
In conclusion, in this work we have discussed tachyonic inflation in the high energy RS-II Braneworld scenario in the light of the swampland conjectures and considered the possibility of swampland consistent eternal inflation in this regime. We started off by describing why tachyonic inflation in this particular scenario could possibly be one of the most suited arenas for the swampland conjectures and hence, might allow for the possibility of evading the swampland issues eternal inflation too. Then after describing some basics of Tachyonic inflation in this regime, we showed that this inflationary model is virtually unscathed by the swampland conjectures and can quite intrinsically evade all the prominent swampland issues which have been discussed for regular single field inflation, as they only imply a lower bound on the inflation energy scale which can be easily satisfied in the considered high energy limit. We then cast our glance towards eternal inflation in this scenario, and discussed the two main swampland issues in this context where we firstly addressed the curvature amplitude issue. We showed that the basic eternal inflation requirement of quantum fluctuations dominating over classical field evolution does not set unavoidable constraints on tachyonic models of any kind and in particular, inflation in high energy RS-II Braneworld. We hence showed that the issues of inconsistency of the dS and refined dS conjectures with the perturbation requirement do not hold good for our tachyonic regime. We then discussed the conflict of entropy bounds with the dS conjecture and showed that our concerned inflationary regime does not have any issues with the entropy bound even when the concerned entropy formalism is the standard Bekenstein-Gibbons-Hawking one, as the lower limit on the energy scale implied for consistency with the bound is well within the range needed for consistency with basic inflationary swampland issues. Then made the case as to why it would be better suited if we consider quantum corrections to the BGH entropy , and in particular we considered a Generalized Uncertainty Principle corrected entropy formalism. In order to focus on this particular correction to the entropy, we only considered the leading order GUP corrections to the entropy and showed that a GUP formalism of the entropy allows one to evade the entropy bound issues in both tachyonic inflation in our concerned scenario and even in a usual single field model in a GR based cosmology. This allowed us to make a startling observation that a generalized uncertainty principle actually facilitates one to have a swampland (and hence possibly, a quantum gravitationally) consistent picture of eternal inflation and a Multiverse. An important thing to note is that we have not carried out a detailed analysis of eternal inflation in any kind of a tachyonic regime as we have just focused on showing how the prominent swampland-eternal inflation issues can be resolved in a more quantum gravitationally / String theory motivated setting. Indeed, we have not embarked on exploring the solutions of the Fokker-Planck / Langevin equations for quantum fluctuations of the inflaton field for different potentials, which is more of a standard procedure in the subject. Hence, there might be more model dependent requirements for eternal inflation to take place in a variety for different potentials that we have not taken into account here ( like the model dependent analysis which was done in 117 ) as our explorations have been of a more general nature focused on the prevalent swampland issues currently.
would also like to thank the reviewers of the manuscript for their insightful comments on the paper, which has increased the depth of the work by multi folds.