Holographic Space-time from the Big Bang to the de Sitter era
T. Banks
备注：
30 pages, LaTeX, Expanded version of a lecture given at the Conference on Liouville Quantum Gravity and Statistical Systems, in honor of Alexei Zamolodchikov, Poncelet Institute, Moscow
I review the holographic theory of space-time and its applications to cosmology. Much of this has appeared before, but the discussion is more unified and concise. I also include some material on work in progress, whose aim is to understand compactification in terms of finite dimensional super-algebras. This is an expanded version of a lecture I gave at the conference on Liouville Quantum Gravity and Statistical Systems, in memory of Alexei Zamolodchikov, at the Poncelet Institute in Moscow, 21-24 June, 2008.
In view of our accelerating universe, one of the outstanding theoretical issues is the absence of a quantum-gravitational description of de Sitter space. Although speculative, an intriguing circumvention may be found in the realm of brane-world scenarios; where the physical universe can be interpreted as a non-critical 3-brane moving in a higher-dimensional, static bulk. In this paper, we focus on the cosmological implications of a positively curved brane world evolving in the background of a ``topological'' anti-de Sitter black hole (i.e, Schwarzschild-like but with an arbitrary horizon topol…
Using the Einstein-Hilbert approximation of asymptotically safe quantum gravity we present a consistent renormalization group based framework for the inclusion of quantum gravitational effects into the cosmological field equations. Relating the renormalization group scale to cosmological time via a dynamical cutoff identification this framework applies to all stages of the cosmological evolution. The very early universe is found to contain a period of ``oscillatory inflation'' with an infinite sequence of time intervals during which the expansion alternates between acceleration and deceleratio…
A quantum state of the entire cosmos (universe or multiverse) is proposed which is the equal mixture of the Giddings-Marolf states that are asymptotically single de Sitter spacetimes in both past and future and are regular on the throat or neck of minimal three-volume. That is, states are excluded that have a big bang or big crunch or which split into multiple asymptotic de Sitter spacetimes. (For simplicity, transitions between different values of the cosmological constant are assumed not to occur, though different positive values are allowed.) The entropy of this mixed state appears to be of…
We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. Depending on the parameters, either a first or second order phase transition can occur. In the first case, an instanton allows a double analytic continuation. It induces a probability to enter the inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure d…
Existence and stability analysis of the Kantowski-Sachs type inflationary universe in a higher derivative scalar-tensor gravity theory is studied in details. Isotropic de Sitter background solution is shown to be stable against any anisotropic perturbation during the inflationary era. Stability of the de Sitter space in the post inflationary era can also be realized with proper choice of coupling constants.
In this work we examine the effects of a pre-inflationary de Sitter bounce on the energy spectrum of the primordial gravitational waves. Specifically we assume that the Universe is described by several evolution patches, starting with a de Sitter pre-inflationary bounce which is followed by an quasi-de Sitter slow-roll inflationary era, followed by a constant equation of state parameter abnormal reheating era, which is followed by the radiation and matter domination eras and the late-time acceleration eras. The bounce and the inflationary era can be realized by vacuum $f(R)$ gravity and the ab…
Following up an earlier suggestion of how the Tolman Entropy Conundrum (TEC) can be solved in a cyclic cosmology using the Come Back Empty (CBE) assumption with phantom dark energy, here we show how the same CBE strategy may work with a cosmological constant in the expansion era. As in the earlier case, this leads to a multiverse, actually an infiniverse, with the concomitant issues of predictivity and testability. Here we show how extreme flatness and homogeneity at the bounce are natural properties of the contraction era, interestingly without any necessity for an inflationary era at the beg…
We investigate infrared logarithms in de Sitter space from holographic perspective. We employ a gravitational Fokker-Planck equation to investigate the time evolution of the de Sitter entropy $S=π/(G_N H^2)$, where $H$ is the Hubble parameter and $G_N$ is the Newton's constant. Under the Gaussian approximation, we obtain the dynamical $β$ function of $g=1/S$. It is asymptotically free toward the future. It also possesses the ultraviolet fixed point indicating that the Universe started the de Sitter expansion at the Planck scale. The pre-inflation era exists to prepare a special initial conditi…
The current cosmic acceleration does not imply that our Universe is basically de Sitter-like: in the first part of this work we argue that, by introducing matter into *anti-de Sitter* spacetime in a natural way, one may be able to account for the acceleration just as well. However, this leads to a Big Crunch, and the Euclidean versions of Bang/Crunch cosmologies have [apparently] disconnected conformal boundaries. As Maldacena and Maoz have recently stressed, this seems to contradict the holographic principle. In the second part we argue that this "double boundary problem" is a matter not of g…
We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sense that entire spatial slices become visible to a comoving observer before the end of conformal time, while the accelerating big-bang geometries can be either short or tall. We consider the interpretation of these cosmological sol…
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a …
We discuss the mechanism of reheating in pre-big bang string cosmology and we calculate the amount of moduli and gravitinos produced gravitationally and in scattering processes of the thermal bath. We find that this abundance always exceeds the limits imposed by big-bang nucleosynthesis, and significant entropy production is required. The exact amount of entropy needed depends on the details of the high curvature phase between the dilaton-driven inflationary era and the radiation era. We show that the domination and decay of the zero-mode of a modulus field, which could well be the dilaton, or…
The pre-big-bang cosmology inspired by superstring theories has been suggested as an alternative to slow-roll inflation. We analyze, in both the Jordan and Einstein frames, the effect of spatial curvature on this scenario and show that too much curvature --- of either sign --- reduces the duration of the inflationary era to such an extent that the flatness and horizon problems are not solved. Hence, a fine-tuning of initial conditions is required to obtain enough inflation to solve the cosmological problems.
We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We …
There have been many attempts to construct de Sitter space-times in string theory. While arguably there have been some successes, this has proven challenging, leading to the de Sitter swampland conjecture: quantum theories of gravity do not admit stable or metastable de Sitter space. Here we explain that, within controlled approximations, one lacks the tools to construct de Sitter space in string theory. Such approximations would require the existence of a set of (arbitrarily) small parameters, subject to severe constraints. But beyond this one also needs an understanding of big-bang and big-c…
General non-singular accelerating cosmological solutions for an initial cosmic period of pure vacuum birth era are derived. This vacuum era is described by a varying cosmological "constant" suggested by the Renormalisation Group flow of Asymptotic Safety scenario near the ultraviolet fixed point. In this scenario, natural exit from inflation to the standard decelerating cosmology occurs when the energy scale lowers and the cosmological "constant" becomes insignificant. In the following period where matter is also present, cosmological solutions with characteristics similar to the vacuum case a…
We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(ρ, s=\frac 12)\,$ representation of the de Sitter group. We find that time has peculiar property: it is not self-adjoint, but appropriate restrictions to the space of physical states give self-adjoint extensions. Extensions have discrete spectrum with logarithmic distribution of eigenvalues, $\,t_n \sim \ell\, \log\, n$+const, where $\ell$ characterizes noncommutativity and the usual assumption is $\,\ell=\ell_{Planck}$. When calculated on physical states, radius of the universe is b…
In the recently proposed cosmological constant (CC) filter mechanism based on modified gravity in the Palatini formalism, gravity in the radiation, matter and late-time de Sitter eras is insensitive to energy sources with the equation of state -1. This implies that finite vacuum energy shifts from phase transitions are filtered out, too. In this work we investigate the CC filter model at very early times. We find that the initial big bang singularity is replaced by a cosmic bounce, where the matter energy density and the curvature are finite. In a certain case this finiteness can be observed a…
A regular bouncing universe is obtained in the context of a dilaton-gravity brane world scenario. The scale factor starts in a contracting inflationary phase both in the Einstein and in the string frame, it then undergoes a bounce (due to interaction with the bulk Weyl tensor), and subsequently enters into a decelerated expanding era. This graceful exit is obtained at low curvature and low coupling, and without violating the Null Energy Condition.
We discuss JT gravity in AdS and dS space in the second order formalism. For the pure dS JT theory without matter, we show that the path integral gives rise in general to the Hartle-Hawking wave function which describes an arbitrary number of disconnected universes produced by tunnelling "from nothing", or to transition amplitudes which describe the tunnelling of an initial state consisting of several contracting universes to a final state of several expanding universes. These processes can be described by a hologram consisting of Random Matrix Theory (RMT) or, we suggest, after some modificat…
A general form of quasi-de Sitter(dS) modes in a dynamical background is used to study the creation of particle during the inflation. Actually, by considering the general form of inflaton field equation as a function of the Hankel function index and by using the Planck 2015 constraint on spectral index, we obtain the possible new constraints for the values of coupling constant in the era with quasi-dS space-time. Then, we explicitly calculate the general form of expectation value of the created particles in terms of the Hankel function index and the conformal time. As an important result, we s…
We generalize previous work on inhomogeneous pre-big bang cosmology by including the effect of non-trivial moduli and antisymmetric-tensor/axion fields. The general quasi-homogeneous asymptotic solution---as one approaches the big bang singularity from perturbative initial data---is given and its range of validity is discussed, allowing us to give a general quantitative estimate of the amount of inflation obtained during the perturbative pre-big bang era. The question of determining early-time ``attractors'' for generic pre-big bang cosmologies is also addressed, and a motivated conjecture is …
The apparent observation of dark energy poses problems for string theory. In de Sitter space, or in quintessence models, one cannot define a gauge-invariant S-matrix. We argue that eternal quintessence does not arise in weakly coupled string theory, but point out that it is difficult to define an $S$-matrix even in the presence of perturbative potentials for the moduli. The solutions of the Fischler-Susskind equations all have Big Bang or Big Crunch Singularities. We believe that an S-matrix (or S-vector) exists in this context but cannot be calculated by purely perturbative methods. We study …
To gain insight in the quantum nature of the big bang, we study the dual field theory description of asymptotically anti-de Sitter solutions of supergravity that have cosmological singularities. The dual theories do not appear to have a stable ground state. One regularization of the theory causes the cosmological singularities in the bulk to turn into giant black holes with scalar hair. We interpret these hairy black holes in the dual field theory and use them to compute a finite temperature effective potential. In our study of the field theory evolution, we find no evidence for a "bounce" fro…
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS_3, the solutions are invariantly characterized by their holonomies. We show that the dS_3 quotient singularity can be de-singularized by an SL(3,C) gauge transformation tha…
We review the advanced version of the KKLT construction and pure $d=4$ de Sitter supergravity, involving a nilpotent multiplet, with regard to various conjectures that de Sitter state cannot exist in string theory. We explain why we consider these conjectures problematic and not well motivated, and why the recently proposed alternative string theory models of dark energy, ignoring vacuum stabilization, are ruled out by cosmological observations at least at the $3σ$ level, i.e. with more than $99.7\%$ confidence.
We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto t$ is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era.
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
Oscillations of the $F(R)$ dark energy around the phantom divide line, $ω_{DE}=-1$, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the $F(R)$-functions in terms of the dark energy pertu…
We calculate the density and gravitational wave spectrums generated in a version of string cosmology termed pre-big bang scenario. The large scale structures are originated from quantum fluctuations of the metric and dilaton field during a pole-like inflation stage driven by a potential-less dilaton field realized in the low-energy effective action of string theory. The generated classical density field and the gravitational wave in the second horizon crossing epoch show tilted spectrums with n ~ 4 and n_T ~ 3, respectively. These differ from the observed spectrum of the large angular scale an…
Yang-Mills theory with flavor quarks in the dS${}_4$ is studied through the dual supergravity in the AdS${}_5\times S^5$ background with non-trivial dilaton and axion. The flavor quarks are introduced by embedding a probe D7 brane. We find that the dynamical properties of YM theory in the dS${}_4$ are similar to the case of the finite temperature theory given by the 5d AdS-Schwarzschild background. In the case of dS${}_4$, however, contrary to the finite temperature case, the gauge field condensate plays an important role on the dynamical properties of quarks. We also give the quark-antiquark …
Using entanglement in dS/CFT correspondence, we show that a 4-dimensional de Sitter spacetime in the bulk fluctuates. We calculated the fluctuations of the entanglement entropy, which backreacts with the geometry of the bulk spacetime indicated by the fluctuations of the horizon radius. The variance of the fluctuations is suppressed by $G_N$ and multiplied by $H_{dS}^2$. Therefore, it will be more significant during the primordial era where it is also well described by de Sitter geometry. We also show that the distribution of the fluctuations is also skewed with the local non-linearity paramet…
In the framework of superstring compactifications with N=1 supersymmetry spontaneously broken, (by either geometrical fluxes, branes or else), we show the existence of new inflationary solutions. The time-trajectory of the scale factor of the metric a, the supersymmetry breaking scale m=m(Phi) and the temperature T are such that am and aT remain constant. These solutions request the presence of special moduli-fields: i) The universal "no-scale-modulus" Phi, which appears in all N=1 effective supergravity theories and defines the supersymmetry breaking scale m(Phi). ii) The modulus Phi_s, which…
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an early-time period of de Sitter expansion followed by a radiation-dominated era and track the evolution of complexity throughout this history. During early-time de Sitter expansion the complexity grows linearly with the number of e-folds for modes outside the horizon. The evolution of complexity also suggests that the Universe behaves like a chaotic system duri…
Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti-de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study 4-dimensional gravitational path integrals in the presence of a negative cosmological constant, and with minisuperspace metrics. We…
A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $Λ\approx H^4$, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with $H \approx 1$. However, at a given time, the expansion undertakes a phase transition, with H and $Λ$ decreasing to nearly zero in a few Planck times, producin…
We explore the cosmological dynamics of an effective f(R) model constructed from a renormalisation group (RG) improvement of the Einstein--Hilbert action, using the non-perturbative beta functions of the exact renormalisation group equation. The resulting f(R) model has some remarkable properties. It naturally exhibits an unstable de Sitter era in the ultraviolet (UV), dynamically connected to a stable de Sitter era in the IR, via a period of radiation and matter domination, thereby describing a non-singular universe. We find that the UV de Sitter point is one of an infinite set, which make th…
We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on the exponent of Barrow entropy. The latter is an extended entropy relation arising from the incorporation of quantum-gravitational effects on the black-hole structure, parameterized effectively by the new parameter $Δ$. When considered in a cosmological framework and under the light of the gravity-thermodynamics conjecture, Barrow entropy leads to modified cosmological scenarios whose Friedmann equations contain extra terms. We perform a detailed analysis of the BBN era and we calculate the deviation of the freeze-out…
Constraining Early Dark Energy cosmological models with Big Bang Nucleosynthesis
Astronomical Institute of Romanian Academy, Cluj-Napoca Branch（罗马尼亚科学院天体物理研究所）；Babeş-Bolyai University（博拜-鲍约什大学）；Technical University of Cluj-Napoca（克卢日-纳波卡理工大学）
If the Standard Model (SM) Higgs is weakly coupled to the inflationary sector, the Higgs is expected to be universally in the form of a condensate towards the end of inflation. The Higgs decays rapidly after inflation - via non-perturbative effects - into an out-of-equilibrium distribution of SM species, which thermalize soon afterwards. If the post-inflationary equation of state of the universe is stiff, $w \simeq +1$, the SM species eventually dominate the total energy budget. This provides a natural origin for the relativistic thermal plasma of SM species, required for the onset of the `hot…
We investigate the idea that the universe before the Big Bang is the $CPT$ reflection of the universe after the bang, both classically and quantum mechanically, so that the universe does {\it not} spontaneously violate $CPT$. We show how $CPT$ symmetry selects a preferred vacuum state for quantum fields on a $CPT$-invariant cosmological background spacetime. The universe before the bang and the universe after the bang may be viewed as a universe/anti-universe pair, emerging directly into the hot, radiation-dominated era we observe in our past. This, in turn, leads to a remarkably economical ex…
Central European Institute for Cosmology and Fundamental Physics (CEICO), Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所中欧宇宙学与基础物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学大学院理学研究系早期宇宙研究中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学前沿研究机构宇宙物理与数学卡弗里研究所）；Institut d’Astrophysique de Paris, UMR-7095 du CNRS（巴黎天体物理研究所法国国家科学研究中心联合研究实验室）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The…
The background cosmological dynamics of the late Universe is analysed on the framework of a dark energy model described by an holographic Ricci dark energy component. Several kind of interactions between the dark energy and the dark matter components are considered herein. We solve the background cosmological dynamics for the different choices of interactions with the aim to analyse not only the current evolution of the universe but also its asymptotic behaviour and, in particular, possible future singularities removal. We show that in most of the cases, the Big Rip singularity, a finger print…
The vacuum $R^2$ model is known to generate a quasi-de Sitter evolution for inflation, using solely the slow-roll assumptions. Using standard reconstruction techniques, we demonstrate that the $f(R)$ gravity which actually realizes the quasi-de Sitter evolution is not simply the $R^2$ model but a deformed $R^2$ model which contains extra terms in addition to the $R^2$ model. We analyze in detail the inflationary dynamics of the deformed $R^2$ model and we demonstrate that the predictions are quite close to the ones of the pure $R^2$ model, regardless the values of the free parameters. Basicall…
Milne-like spacetimes are a class of FLRW models which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something physical may have happened there. Next we ask what role these spacetimes have in modern cosmology. We find that Milne-like spacetimes are inconsistent with classical cosmology theory in which a radiation-dominated era follows immediately after the big bang. However, Milne-like space…
The purpose of this work is to use a renormalized quantum scalar field to investigate very early cosmology, in the Planck era immediately following the big bang. Renormalization effects make the field potential dependent on length scale, and are important during the big bang era. We use the asymptotically free Halpern-Huang scalar field, which is derived from renormalization-group analysis, and solve Einstein's equation with Robertson-Walker metric as an initial-value problem. The main prediction is that the Hubble parameter follows a power law: $H\equiv\dot{a}/a\sim t^{-p}$, and the universe …
Ultraviolet Completion of the Big Bang in Quadratic Gravity
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（珀米特理论物理研究所）；Waterloo Centre for Astrophysics, University of Waterloo（滑铁卢大学天体物理中心）；École de technologie supérieure, Université du Québec（魁北克理工大学）；McGill University（麦吉尔大学）
We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cut-off at the one-loop level. The scale invariant spectrum in the gravitational propagator at the super-horizon scale is the source of the de Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become time dependent and diminish with time. In contrast, the Newton's constant increases with time. We clarify the physical mechanism behind these effects in terms…
According to theoretical physics the cosmological constant (CC) is expected to be much larger in magnitude than other energy densities in the universe, which is in stark contrast to the observed Big Bang evolution. We address this old CC problem not by introducing an extremely fine-tuned counterterm, but in the context of modified gravity in the Palatini formalism. In our model the large CC term is filtered out, and it does not prevent a standard cosmological evolution. We discuss the filter effect in the epochs of radiation and matter domination as well as in the asymptotic de Sitter future. …
Within two specific string cosmology scenarios --differing in the way the pre- and post-big bang phases are joined-- we compute the size and spectral slope of various types of cosmologically amplified quantum fluctuations that arise in generic compactifications of heterotic string theory. By further imposing that these perturbations become the dominant source of energy at the onset of the radiation era, we obtain physical bounds on the background's moduli, and discuss the conditions under which both a (quasi-) scale-invariant spectrum of axionic perturbations and sufficiently large seeds for t…
In this paper, we shall consider $f(R)$ gravity and its cosmological implications, when an extra matter term generated by thermal effects is added by hand in the Lagrangian. We formulate the equations of motion of the theory as a dynamical system, that can be treated as an autonomous one only for specific solutions for the Hubble rate, which are of cosmological interest. Particularly, we focus our analysis on subspaces of the total phase space, corresponding to (quasi-)de Sitter accelerating expansion, matter-dominated and radiation-dominated solutions. In all the aforementioned cases, the dyn…
We investigate pair creation by an electric field in four-dimensional de Sitter space. The expectation value of the induced current is computed, using the method of adiabatic regularization. Under strong electric fields the behavior of the current is similar to that in flat space, while under weak electric fields the current becomes inversely proportional to the mass squared of the charged field. Thus we find that the de Sitter space obtains a large conductivity under weak electric fields in the presence of a charged field with a tiny mass. We then apply the results to constrain electromagneti…
The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the Big Bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity-free for certain region of the parameter space in which the divergence of the Hubble rate at the high energy regime is substituted by a de-Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe, cosmological singularities such as Big Rip, Big Bang, Big Freez…
