We analyse slow-roll inflationary cosmologies that are holographically dual to a three-dimensional conformal field theory deformed by a nearly marginal scalar operator. We show the cosmological power spectrum is inversely proportional to the spectral density associated with the 2-point function of the trace of the stress tensor in the deformed CFT. Computing this quantity using second-order conformal perturbation theory, we obtain a holographic power spectrum in exact agreement with the expected inflationary power spectrum to second order in slow roll.
We show how to derive several families of accelerating universe solutions to an Einstein-Aether gravity theory. These solutions provide possible descriptions of inflationary behaviour in the early universe and late-time cosmological acceleration.
The Fermi Paradox is discussed in the light of the inflationary and brane world cosmologies. We conclude that some brane world cosmologies may be of relevance for the problem of civilizations spreading across our galaxy, strengthening the Fermi Paradox, but not the inflationary cosmologies, as has been proposed.
We consider the question of deriving initial conditions for scalar fields in driving both an early and late quintessence phase. The dark energy field presents an unresolved uniformity problem. Further difficulties with initial conditions for assisted, kinetic and phantom inflation are presented. We review the use of the canonical measure and find the negative conclusions of Gibbons and Hawking can be allayed by means of a reasonable quantum cosmological input. We remark upon some attempts at incorporating inflationary schemes into cyclic and bouncing models.
We use the three-year WMAP observations to determine the normalization of the matter power spectrum in inflationary cosmologies. In this context, the quantity of interest is not the normalization marginalized over all parameters, but rather the normalization as a function of the inflationary parameters n and r with marginalization over the remaining cosmological parameters. We compute this normalization and provide an accurate fitting function. The statistical uncertainty in the normalization is 3 percent, roughly half that achieved by COBE. We use the k-l relation for the standard cosmologica…
The results from Planck2015, when combined with earlier observations from WMAP, ACT, SPT and other experiments, were the first observations to disfavor the "classic" inflationary paradigm. To satisfy the observational constraints, inflationary theorists have been forced to consider plateau-like inflaton potentials that introduce more parameters and more fine-tuning, problematic initial conditions, multiverse-unpredictability issues, and a new 'unlikeliness problem.' Some propose turning instead to a "postmodern" inflationary paradigm in which the cosmological properties in our observable unive…
With the growing consensus on simple power law inflation models not being favored by the PLANCK observations, dynamics for the non-standard inflation gain significant interest in the recent past. In this paper, we analyze in detail a class of supergravity inspired phenomenological inflationary models with non-polynomial potential based on Maity (Nucl.Phys. B919 (2017) 560), and compare the model predictions with the currently most favored Starobinsky and its generalized $α$-attractor models in the ($n_s$ , $r$) plane constrained by PLANCK. Importantly for a wide range of parameter space, our m…
We calculate the gravitational waves (GW) spectrum produced in various Early Universe scenarios from gauge field sources, thus generalizing earlier inflationary calculations to bouncing cosmologies. We consider generic couplings between the gauge fields and the scalar field dominating the energy density of the Universe. We analyze the requirements needed to avoid a backreaction that will spoil the background evolution. When the scalar is coupled only to $F \tilde F$ term, the sourced GW spectrum is exponentially enhanced and parametrically the square of the vacuum fluctuations spectrum, ${\cal…
We present a new method to calculate the spectrum of (slow-roll) inflationary perturbations, inspired by the conjectured dS/CFT correspondence. We show how the standard result for the spectrum of inflationary perturbations can be obtained from deformed CFT correlators, whose behavior is determined by the Callan-Symanzik equation. We discuss the possible advantages of this approach and end with some comments on the role of holography in dS/CFT and its relation to the universal nature of the spectrum of inflationary perturbations.
We review the recent developments in obtaining accelerating cosmologies and/or inflation from higher-dimensional gravitational theories, in particular superstring theories in ten dimensions and M-theory in eleven dimensions. We first discuss why it is difficult to obtain inflationary behavior in the effective low-energy theories of superstring/M-theory, i. e. supergravity theories. We then summarize interesting solutions including S-branes that give rise to accelerating cosmologies and inflationary solutions in M-theory with higher order corrections. Other approaches to inflation in the string…
We study the onset of inflation in 3+1 dimensional cosmologies with an inflationary potential $U$ satisfying $0 < Λ_1 \leq U \leq Λ_2$, matter satisfying the dominant and strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are orbits under an isometry group. Assuming an initial Cauchy slice with positive mean curvature everywhere, we show, via mean curvature flow, that there exists a family of spatial slices parameterized by $λ$, whose volume grows between the flat slicings in de Sitter spaces with cosmological constants $Λ_1$ and $Λ_2$. In par…
We consider the compactification of (d+n)-dimensional pure gravity and of superstring/M-theory on an n-dimensional internal space to a d-dimensional FLRW cosmology, with spatial curvature k=-1,0,+1, in Einstein conformal frame. The internal space is taken to be a product of Einstein spaces, each of which is allowed to have arbitrary curvature and a time-dependent volume. By investigating the effective d-dimensional scalar potential, which is a sum of exponentials, it is shown that such compactifications, in the k=0,+1 cases, do not lead to large amounts of accelerating expansion of the scale f…
In order to study the effect of the anti de Sitter/ conformal field theory correspondence (AdS/CFT) on the primordial inflationary era, we consider a universe filled with a tachyon field in a slow-roll regime. In this context, the background and perturbative parameters characterising the inflationary era are related to the standard one by correction terms. We show a clear agreement between the theoretical prediction and the observational data for the above mentioned model. The main results of our work are illustrated for an exponential potential. We show that, for a suitable conformal anomaly …
We consider BTZ black holes and flat space cosmologies in generic higher derivative gravity theories in 2+1 dimensions. Our goal is to prove the match between the bulk Iyer-Wald entropy and the field theory entropy for various symmetry algebras (CFT$_2$, Warped CFT$_2$, BMS$_3$). We also discuss phase transitions in higher curvature theories, and argue that, in the flat case, there is strictly speaking no phase transition in the grand canonical ensemble.
We use the dS/CFT correspondence and bulk gravity to predict the form of the renormalized holographic three-point correlation function of the operator which is dual to the inflaton field perturbation during single-field, slow-roll inflation. Using Maldcaena's formulation of the correspondence, this correlator can be related to the three-point function of the curvature perturbation generated during single-field inflation, and we find exact agreement with previous bulk QFT calculations. This provides a consistency check on existing derivations of the non-Gaussianity from single-field inflation a…
In this paper, we use a known duality between expanding and contracting cosmologies to construct a dual of the inflationary flow hierarchy applicable to contracting cosmologies such as Ekpyrotic and Cyclic models. We show that the inflationary flow equations are invariant under the duality and therefore apply equally well to inflation or to cyclic cosmology. We construct a self-consistent small-parameter approximation dual to the slow-roll approximation in inflation, and calculate the power spectrum of perturbations in this limit. We also recover the matter-dominated contracting solution of Wa…
Recent observations suggest that the cosmological equation-of-state parameter w is close to -1. To say this is to imply that w could be slightly less than -1, which leads to R.Caldwell's "Phantom cosmologies". These often have the property that they end in a "Big Smash", a final singularity in which the Universe is destroyed in a finite proper time by excessive *expansion*. We show that, classically, this fate is not inevitable: there exist Smash-free Phantom cosmologies, obtained by a suitable perturbation of the deSitter equation of state, in which the spacetime is in fact asymptotically deS…
The creation of 4d de Sitter (inflationary) boundary gluing two d5 de Sitter bulks on the classical as well as on quantum level (with account of brane QFT via corresponding trace anomaly induced effective action) is discussed. Quantum effects decrease the classical de Sitter brane radius or create new de Sitter brane with even smaller radius. It is important that brane CFT may be chosen to be dual to one of 5d de Sitter bulks, making the explicit relation of de Sitter brane-world with dS/CFT correspondence. In this way, the localization of gravity on the brane is shown. Moving (time-dependent)…
We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe.
In this paper we establish dualities between inflationary, cyclic/ekpyrotic, and phantom cosmologies within the patch formalism approximating high-energy effects in scenarios with extra dimensions. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts; the dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane. We then address some qualitative issues about phantomlike cosmologies without phantom matter.
We present a general slow-roll formalism within braneworld-motivated cosmologies with non-standard effective Friedmann equations. Full towers of parameters involving either the inflaton potential or the Hubble parameter are constructed and the dynamics of non-tachyonic and tachyonic fields are considered in detail; exact cosmological solutions and the inflationary attractor condition are provided. We compare scalar-driven and tachyon-driven accelerating eras through slow-roll correspondence and the observational imprint on early-universe structures.
An inflationary epoch driven by the kinetic energy density in a dynamical Planck mass is studied. In the conformally related Einstein frame it is easiest to see the demands of successful inflation cannot be satisfied by kinetic inflation alone. Viewed in the original Jordan-Brans-Dicke frame, the obstacle is manifest as a kind of graceful exit problem and/or a kind of flatness problem. These arguments indicate the weakness of only the simplest formulation. {}From them can be gleaned directions toward successful kinetic inflation.
Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular spacetimes with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary …
The role of conformal anomaly in AdS/CFT and related issues is clarified. The comparison of holographic and QFT conformal anomalies (with account of brane quantum gravity contribution) indicates on the possibility for brane quantum gravity to occur within AdS/CFT set-up. 3d quantum induced inflationary (or hyperbolic) brane-world is shown to be realized in frames of AdS3/CFT2 correspondence where the role of 2d brane cosmological constant is played by effective tension due to two-dimensional conformal anomaly. The dynamical equations to describe 4d FRW-Universe with account of quantum effects …
In this work we develop the patch formalism, an approach providing a very simple and compact description of braneworld-motivated cosmologies with nonstandard effective Friedmann equations. In particular, the Hubble parameter is assumed to depend on some power of the brane energy density, H^2 \propto ρ^q. The high-energy limit of Randall-Sundrum (q=2) and Gauss-Bonnet (q=2/3) braneworlds are considered, during an accelerating era triggered by a single ordinary or tachyonic scalar field. The inflationary dynamics, solutions, and spectra are provided. Using the latest results from WMAP and other …
Based on the effective field theory (EFT) of nonsingular cosmologies, we build a stable model, without the ghost and gradient instabilities, of bounce inflation (inflation is preceded by a cosmological bounce). We perform a full simulation for the evolution of scalar perturbation, and find that the perturbation spectrum has a large-scale suppression (as expected), which is consistent with the power deficit of the cosmic microwave background (CMB) TT-spectrum at low multipoles, but unexpectedly, it also shows itself one marked lower valley, which actually provides a better fit to the dip at mul…
In this work we revisit Wald's cosmic no-hair theorem in the context of accelerating Bianchi cosmologies for a generic cosmic fluid with non-vanishing anisotropic stress tensor and when the fluid energy momentum tensor is of the form of a cosmological constant term plus a piece which does not respect strong or dominant energy conditions. Such a fluid is the one appearing in inflationary models. We show that for such a system anisotropy may grow, in contrast to the cosmic no-hair conjecture. In particular, for a generic inflationary model we show that there is an upper bound on the growth of an…
Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). {\it All} semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular spacetimes with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflati…
We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spe…
We build a number of integrable one--scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non--integrable ones. These include the need for the scalar to emerge from the initial singularity while climbing up sufficiently steep exponential potentials ("climbing phenomenon") and the inevitable collapse in a big Crunch whenever the scalar tries to settle at negative extrema of the p…
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\partial_μϕ\partial^μϕ)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We co…
The general model of higher derivative (HD) gravity is considered. The search of brane-world cosmology in such theory is presented when bulk is d5 AdS and boundary is spherical, hyperbolic or flat (single) brane. It is found the wide range of theory parameters where such cosmology may be realized. Special attention is paid to the version of HD theory representing SG dual of ${\cal N}=2$ $Sp(N)$ SCFT (in next-to-leading order of large $N$ expansion). In particular, it is shown that inflationary brane Universe does not occur for SG dual while hyperbolic brane occurs (which was not possible in le…
We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state $p=ρ$. The recently proposed Holographic Universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the $p=ρ$ fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector pertu…
We show a model-independent fine-tuning issue in the DBI inflationary mechanism. DBI inflation requires a warp factor h small enough to sufficiently slow down the inflaton. On the other hand, the Einstein equation in extra dimensions under the inflationary background deforms the warp space in the IR side. Generically these two locations coincide with each other, spoiling the DBI inflation. The origin and tuning of this ``h-problem'' is closely related, through the AdS/CFT duality, to those of the well-known ``eta-problem'' in the slow-roll inflationary mechanism.
We study phantom and inflationary cosmologies using form-invariance transformations of the Einstein equations with respect to $ρ$, $H$, $a$ and $p$, from a 5D vacuum. Equations of state and squared fluctuations of the inflaton and phantom fields are examined.
We present an overview of the recently suggested cosmological model driven by conformal field theory (CFT) with the initial conditions in the form of the microcanonical density matrix. In particular, we discuss the origin of inflationary stage in this model and a novel feature -- the thermal nature of the primordial power spectrum of the CMB anisotropy. The relevant effect of "temperature of the relic temperature anisotropy" can be responsible for a thermal contribution to the red tilt of this spectrum, additional to its conventional vacuum component. The amplification of this effect due to re…
We analyze flat FRW cosmologies and hyperscaling-violating geometries by emphasizing the analytic continuation between them and their scale covariance. We exhibit two main calculations where this point of view is useful. First, based on the scale covariance, we show that the structure of higher curvature corrections to Einstein's equation is very simple. Second, in the context of accelerated FRW cosmologies, also known as Q-space, we begin by calculating the Bunch-Davies wavefunctional for a massless scalar field and considering its interpretation as a generating functional of correlation func…
We provide a precise and quantitative holographic description of a class of inflationary slow-roll models. The dual QFT is a deformation of a three-dimensional CFT by a nearly marginal operator, which, in the models we consider, generates an RG flow to a nearby IR fixed point. These models describe hilltop inflation, where the inflaton rolls from a local maximum of the potential in the infinite past (corresponding to the IR fixed point of the dual QFT) to reach a nearby local minimum in the infinite future (corresponding to the UV of the dual QFT). Through purely holographic means, we compute …
During inflation, spacetime is approximately described by de Sitter space which is conformally invariant with the symmetry group SO(1,4). This symmetry can significantly constrain the quantum perturbations which arise in the inflationary epoch. We consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries. Special conformal transformations play an important role in our analysis. Our result applies only to models where the inflaton sector…
We review some general aspects of braneworld cosmologies in which an inflationary period driven by a scalar field confined on the brane is described by a nonstandard effective Friedmann equation. The perturbation spectra, consistency equations and observational consequences of these models are considered.
The role of bulk matter quantum effects (via the corresponding effective potential discussed on the example of conformal scalar) and of boundary matter quantum effects (via the conformal anomaly induced effective action) is considered in brane-world cosmology. Scenario is used where brane tension is not free parameter, and the initial bulk-brane classical action is defined by some considerations. The effective bulk-brane equations of motion are analyzed. The quantum creation of 4d de Sitter or Anti-de Sitter(AdS) brane Universe living in 5d AdS space is possible when quantum bulk and (or) bran…
Holographic inflation posits that the inflationary deSitter era of our universe is approximately described by a dual three-dimensional Euclidean CFT living on the spatial slice at the end of inflation. We point out that the BICEP2 results determine the central charge of this putative CFT to be given by $C_T=1.2 \times 10^9$.
The AdS/CFT correspondence is used to describe five-dimensional cosmology with a big crunch singularity in terms of super-Yang-Mills theory on R times S^3 deformed by a potential which is unbounded below. Classically, a Higgs field in the dual theory rolls to infinity in finite time. But since the S^3 is finite, the unstable mode spreads quantum mechanically and the singularity is resolved when self-adjoint boundary conditions are imposed at infinity. Asymptotic freedom of the coupling governing the instability gives us computational control and the quantum spreading provides a UV cutoff on pa…
