We consider implications of the quantum extension of the inflationary no hair theorem. We show that when the quantum state of inflation is picked to ensure the validity of the EFT of fluctuations, it takes only ${\cal O}(10)$ efolds of inflation to erase the effects of the initial distortions on the inflationary observables. Thus the Bunch-Davies vacuum is a very strong quantum attractor during inflation. We also consider bouncing universes, where the initial conditions seem to linger much longer and the quantum `balding' by evolution appears to be less efficient.
We study an inflationary scenario with a vector field coupled with an inflaton field and show that the inflationary universe is endowed with anisotropy for a wide range of coupling functions. This anisotropic inflation is a tracking solution where the energy density of the vector field follows that of the inflaton field irrespective of initial conditions. We find a universal relation between the anisotropy and a slow-roll parameter of inflation. Our finding has observational implications and gives a counter example to the cosmic no-hair conjecture.
We study inflation with multiple vector fields. In the presence of non-trivial couplings between the inflaton and the vector fields, it turns out that no-hair conjecture does not hold and vector-hair appears. In the case of uniform couplings, nevertheless, we find that the universe approaches an isotropic final state after transient anisotropic inflationary phases. For general couplings, we numerically show attractors are anisotropic inflation. Even in these cases, it turns out that the inflation always tends to minimize the anisotropy in the expansion of the universe.
Gauge-flation, inflation from non-Abelian gauge fields, was introduced in [1,2]. In this work, we study the cosmic no-hair conjecture in gauge-flation. Starting from Bianchi-type I cosmology and through analytic and numeric studies we demonstrate that the isotropic FLRW inflation is an attractor of the dynamics of the theory and that the anisotropies are damped within a few e-folds, in accord with the cosmic no-hair conjecture.
Recently an inflationary model with a vector field coupled to the inflaton was proposed and the phenomenology studied for the Bianchi type I spacetime. It was found that the model demonstrates a counter-example to the cosmic no-hair theorem since there exists a stable anisotropically inflationary fix-point. One of the great triumphs of inflation, however, is that it explains the observed flatness and isotropy of the universe today without requiring special initial conditions. Any acceptable model for inflation should thus explain these observations in a satisfactory way. To check whether the m…
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…
We will present main results of our recent investigations on the validity of cosmic no-hair conjecture proposed by Hawking and his colleagues long time ago in the framework of an anisotropic inflationary model proposed by Kanno, Soda, and Watanabe. As a result, we will show that the cosmic no-hair conjecture seems to be generally violated in the Kanno-Soda-Watanabe model for both canonical and non-canonical scalar fields due to the existence of a non-trivial coupling term between scalar and electromagnetic fields. However, we will also show that the validity of the cosmic no-hair conjecture wi…
We study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. Although the SU(3) gauge field grows at the initial stage of inflation due to the interaction with the inflaton, nonlinear self-couplings in the kinetic term of the gauge field become significant and cause nontrivial dynamics after sufficient growth. We investigate the evolution of the SU(3) gauge field numerically and reveal attractor solutions in the Bianchi type I spacetime. In general cases where all the components of the SU(3) gauge field have the same magnitude initially, th…
Anomalies in recent observational data indicate that there might be some "anisotropic hair" generated in an inflation period. To obtain general information about the effects of this anisotropic hair to inflation models, we studied anisotropic inflation models that involve one vector and one scalar using several types of potentials. We determined the general relationship between the degree of anisotropy and the fraction of the vector and scalar fields, and concluded that the anisotropies behave independently of the potentials. We also generalized our study to the case of multi-directional aniso…
We study the cosmic no-hair in the presence of spin-2 matter, i.e. in bimetric gravity. We obtain stable de Sitter solutions with the cosmological constant in the physical sector and find an evidence that the cosmic no-hair is correct. In the presence of the other cosmological constant, there are two branches of de Sitter solutions. Under anisotropic perturbations, one of them is always stable and there is no violation of the cosmic no-hair at the linear level. The stability of the other branch depends on parameters and the cosmic no-hair can be violated in general. Remarkably, the bifurcation…
Anisotropic inflationary background geometries are analyzed in the context of an extended gauge action where the electric and magnetic susceptibilities are not bound to coincide and depend on the inflaton field. After deriving various classes of solutions with electric and magnetic hairs, we discuss the problem of the initial boundary conditions of the shear parameter and consider a globally neutral plasma as a possible relic of a preinflationary stage of expansion. While electric hairs are washed out by the finite value of the protoinflationary conductivity, magnetic hairs can persist and int…
In this letter we investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common 'potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.
A cosmic no-hair theorem for all initially contracting, spatially homogeneous, orthogonal Bianchi Cosmologies is derived - which shows that all such Universes asymptote to a spatially flat, isotropic Universe with the inclusion of a shear viscous stress. This establishes a new mechanism of isotropisation in a contracting Universe, which does not take recourse to an ekpyrosis-like mechanism using an effective ultra-stiff equation of state fluid, that is, one in which the pressure is much greater than the energy density.
We study inflation with anisotropic hair induced by form fields. In four dimensions, the relevant form fields are gauge (one-form) fields and two-form fields. Assuming the exponential form of potential and gauge kinetic functions, we find new exact power-law solutions endowed with anisotropic hair. We also explore the phase space of anisotropic inflation and find fixed points corresponding to the exact power-law solutions. Moreover, we perform the stability analysis around the fixed points to reveal the structure of the phase space. It turns out that one of the fixed points becomes an attracto…
The Cosmic no hair theorem is studied in anisotropic Bianchi brane models which admit power law inflation with a scalar field. We note that all Bianchi models except Bianchi type IX transit to an inflationary regime and the anisotropy washes out at a later epoch. It is found that in the brane world, the anisotropic universe approaches the isotropic phase via inflation much faster than that in the general theory of relativity. The modification in the Einstein field equations on the brane is helpful for a quick transition to an isotropic era from the anisotropic brane. We note a case where the c…
We examine whether an extended scenario of a two-scalar-field model, in which a mixed kinetic term of canonical and phantom scalar fields is involved, admits the Bianchi type I metric, which is homogeneous but anisotropic spacetime, as its power-law solutions. Then we analyze the stability of the anisotropic power-law solutions to see whether these solutions respect the cosmic no-hair conjecture or not during the inflationary phase. In addition, we will also investigate a special scenario, where the pure kinetic terms of canonical and phantom fields disappear altogether in field equations, to …
We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmologic…
The gravitational energy is examined in asymptotically de Sitter space-times. The positivity will be shown for certain cases. The de Sitter/CFT(dS/CFT) correspondence recently proposed and cosmic no-hair conjecture are testified in the aspect of the gravitational energy. From the holographic renormalization group point of view, the two conjectures are deeply connected with each other.
Quintessential inflation utilises a single scalar field to account for the observations of both cosmic inflation and dark energy. The requirements for modelling quintessential inflation are described and two explicit successful models are presented in the context of $α$-attractors and Palatini modified gravity.
We describe a simple model of chaotic inflation in supergravity where one can easily tune not only the basic cosmological parameters such as n_{s}, r, and f_NL, but also a possible (subdominant) cosmic string contribution to the CMB anisotropy.
In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the Generalized Second Law conjectured by Bousso and Engelhardt, increases up to …
We review the theory of inflationary perturbations. Perturbations at both linear and nonlinear orders are reviewed. We also review a variety of inflation models, emphasizing their signatures on cosmic perturbations.
We give a brief overview of black-hole solutions in four-dimensional supergravity theories and their extremal and supersymmetric limits. We also address problems like cosmic censorship and no-hair theorems in supergravity theories. While supergravity by itself seems not to be enough to enforce cosmic censorship and absence of primary scalar hair, superstring theory may be.
The isotropy and homogeneity of the cosmic microwave background (CMB) favors "scalar driven" early Universe inflationary models. Non-scalar fields, and in particular gauge fields, are on the other hand commonplace in all high energy particle physics models proposed to be at work at the upper bound on energy scale of inflation set by the current CMB observations. In this review we consider the role and consequences, theoretical and observational, that gauge fields can have during inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the le…
We review an inflationary scenario with the anisotropic expansion rate. An anisotropic inflationary universe can be realized by a vector field coupled with an inflaton, which can be regarded as a counter example to the cosmic no-hair conjecture. We show generality of anisotropic inflation and derive a universal property. We formulate cosmological perturbation theory in anisotropic inflation. Using the formalism, we show anisotropic inflation gives rise to the statistical anisotropy in primordial fluctuations. We also explain a method to test anisotropic inflation using the cosmic microwave bac…
The observational status of inflation after the Planck 2013 and 2015 results and the BICEP2/Keck Array and Planck joint analysis is discussed. These pedagogical lecture notes are intended to serve as a technical guide filling the gap between the theoretical articles on inflation and the experimental works on astrophysical and cosmological data. After a short discussion of the central tenets at the basis of inflation (negative self-gravitating pressure) and its experimental verifications, it reviews how the most recent Cosmic Microwave Background (CMB) anisotropy measurements constrain cosmic i…
We quantize linearized Einstein-Hilbert gravity on de Sitter backgrounds in a covariant gauge. We verify the existence of a maximally-symmetric (i.e.de Sitter-invariant) Hadamard state $Ω$ for all globally hyperbolic de Sitter backgrounds in all spacetime dimensions $D \ge 4$ by constructing the state's 2-point function in closed form. This 2-pt function is explicitly maximally symmetric. We prove an analogue of the Reeh-Schlieder theorem for linearized gravity. Using these results we prove a cosmic no-hair theorem for linearized gravitons: for any state in the Hilbert space constructed from $…
We propose an inflationary primordial feature model that can explain both the large and small-scale anomalies in the currently measured cosmic microwave background (CMB) anisotropy spectra, revealing a clip of adventurous history of the Universe during its primordial epoch. Although the model is currently statistically indistinguishable from the Standard Model, we show that future observations such as the Simons Observatory and LiteBIRD will complement each other in distinguishing the model differences due to their accurate E-mode polarization measurements, and the PICO mission, if funded, can…
In this paper, inflationary cosmology is reviewed, paying particular attention to its observational signatures associated with large-scale density perturbations generated from quantum fluctuations. In the most general scalar-tensor theories with second-order equations of motion, we derive the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the nonlinear estimator $f_{\rm NL}$ of primordial non-Gaussianities to confront models with observations of Cosmic Microwave Background (CMB) temperature anisotropies. Our analysis includes models such as potential-driven slow-roll inflatio…
An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 μ$, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, $\partial_t ϕ\simeq μM_p$ with $μr_s \ll 1$ time-independent. Such a time dependence could arise in scalar-tensor theories either from cosmological evolution, or due to the slow motion of the black hole within an asymptotic spatial gradient in the scalar field. Most remarkably, the amount of scalar hair so induced is independent of the s…
We analyze theoretical constraints on the consistency of brane inflation leading to cosmic superstring formation and on the subsequent radiation of these cosmic superstrings. We first investigate the implications of recently elucidated supergravity constraints on models of brane inflation. We show that both D3/D7 and D3/anti-D3 brane inflation are subject to non-trivial constraints. Both models can be shown to satisfy those constraints, but for the case of D3/D7 there may be important consequences for the inflationary mechanism. We then analyze the strong theoretical constraints on the types o…
We investigate the proposed connection between de Sitter spacetime and the MERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overal…
It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the iso…
We study the imprints of anisotropic inflation on the CMB temperature fluctuations and polarizations. The statistical anisotropy stems not only from the direction dependence of curvature and tensor perturbations, but also from the cross correlation between curvature and tensor perturbations, and the linear polarization of tensor perturbations. We show that off-diagonal $TB$ and $EB$ spectrum as well as on- and off-diagonal $TT, EE, BB, TE$ spectrum are induced from anisotropic inflation. We emphasize that the off-diagonal spectrum induced by the cross correlation could be a characteristic sign…
We study some of the cosmological imprints of pre-inflationary particles. We show that each such particle provides a seed for a spherically symmetric cosmic defect. The profile of this cosmic defect is fixed and its magnitude is linear in a single parameter that is determined by the mass of the pre-inflationary particle. We study the CMB and peculiar velocity imprints of this cosmic defect and suggest that it could explain some of the large scale cosmological anomalies.
These lecture notes provide an introduction to cosmic inflation. In particular I will review the basic concepts of inflation, generation of density perturbations, and reheating after inflation.
Standard D-term inflation is studied in the framework of supergravity. D-term inflation produces cosmic strings, however it can still be compatible with CMB measurements without invoking any new physics. The cosmic strings contribution to the CMB data is not constant, nor dominant, contrary to some previous results. Using current CMB measurements, the free parameters (gauge and superpotential couplings, as well as the Fayet-Iliopoulos term) of D-term inflation are constrained.
We show that an inflationary background might be realized by using any p-form non-minimally coupled to gravity. Standard scalar field inflation corresponds to the 0-form case and vector inflation to the 1-form. Moreover, we show that the 2- and 3-form fields are dual to a new vector and scalar inflationary theories where the kinetic terms are non-minimally coupled to gravity.
We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $Λ$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=λ=0.1$) can be achieved in the case of D-term inflation on the brane.
Recently observational lower bounds on the strength of cosmic magnetic fields were reported, based on gamma-ray flux from distant blazars. If inflation is responsible for the generation of such magnetic fields then the inflation energy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl} times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesis models, where B_{obs} is the observed strength of cosmic magnetic fields. The tensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times (B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strengt…
Discovered almost forty years ago, inflation has become the leading paradigm for the early universe. Originally invented to avoid the fine-tuning puzzles of the standard model of cosmology, the so-called hot Big Bang phase, inflation has always been the subject of intense debates. In this article, after a brief review of the theoretical and observational status of inflation, we discuss the criticisms that have been expressed against it and attempt to assess whether inflation can really be viewed as a successful solution to the above mentioned issues.
Towards the end of the brane inflationary epoch in the brane world, cosmic strings (but not texture, domain walls or monopoles) are copiously produced during brane collision. These cosmic strings are D$p$-branes with $(p-1)$ dimensions compactified. We elaborate on this prediction of the superstring theory description of the brane world. Using the data on the temperature anisotropy in the cosmic microwave background, we estimate the cosmic string tension $μ$ to be around $G μ\simeq 10^{-7}$. This in turn implies that the anisotropy in the cosmic microwave background comes mostly from inflation…
Braneworld cosmology supported by a bulk scalar field with an exponential potential is developed. A general class of separable backgrounds for both single and two-brane systems is derived, where the bulk metric components are given by products of world-volume and bulk coordinates and the world-volumes represent any anisotropic and inhomogeneous solution to an effective four-dimensional Brans-Dicke theory of gravity. We deduce a cosmic no hair theorem for all ever expanding, spatially homogeneous Bianchi world-volumes and find that the spatially flat and isotropic inflationary scaling solution …
In this paper we consider a unique model of inflation where the universe undergoes rapid asymmetric oscillations, each cycle lasting millions of Planck time. Over many-many cycles the space-time expands to mimic the standard inflationary scenario. Moreover, these rapid oscillations leave a distinctive periodic signature in ln(k) in the primordial power spectrum, where k denotes the comoving scale. The best fit parameters of the cyclic-inflation model provides a very good fit to the 7-year WMAP data.
Brane inflation in superstring theory predicts that cosmic strings (but not domain walls or monopoles) are produced towards the end of the inflationary epoch. Here, we discuss the production, the spectrum and the evolution of such cosmic strings, properties that differentiate them from those coming from an abelian Higgs model. As D-branes in extra dimensions, some type of cosmic strings will dissolve rapidly in spacetime, while the stable ones appear with a spectrum of cosmic string tensions. Moreover, the presence of the extra dimensions reduces the interaction rate of the cosmic strings in s…
We study the evolution of simple cosmic string loop solutions in an inflationary universe. We show, for the particular case of circular loops, that periodic solutions do exist in a de Sitter universe, below a critical loop radius $R_c H=1/2$. On the other hand, larger loops freeze in comoving coordinates, and we explicitly show that they can survive more $e$-foldings of inflation than point-like objects. We discuss the implications of these findings for the survival of realistic cosmic string loops during inflation, and for the general characteristics of post-inflationary cosmic string network…
In a simple reanalysis of the KKLMMT scenario, we argue that the slow roll condition in the D3-anti-D3-brane inflationary scenario in superstring theory requires no more than a moderate tuning. The cosmic string tension is very sensitive to the conformal coupling: with less fine-tuning, the cosmic string tension (as well as the ratio of tensor to scalar perturbation mode) increases rapidly and can easily saturate the present observational bound. In a multi-throat brane inflationary scenario, this feature substantially improves the chance of detecting and measuring the properties of the cosmic …
The dominant method of energy loss by a loop of cosmic D-strings in models of warped brane inflation is studied. It is shown that the energy loss via Ramond-Ramond field radiation can dominate by many orders of magnitude over the energy radiation via gravitational wave emission. The ratio of these two energy loss mechanisms depends on the energy scale of inflation, the mass scale of string theory and whether it is a single-throat or a multi-throat inflationary scenario. This can have important consequences for the detection of cosmic superstrings in the near future. It is argued that the bound…
We investigate if the observed small and nearly scale-invariant primordial cosmic perturbation, i.e. the perturbation amplitude $P_ζ\sim10^{-9}$ and the spectral index $n_s \simeq 0.965$, is typical in the landscape of vacua after imposing anthropic selections on them. We consider the situation where the universe begins from a metastable vacuum driving a precedent inflation, a curvature-dominated open universe is created by tunneling, and the curvature energy is inflated away by new inflation. We argue that the initial inflaton field value is homogeneous but typically non-zero because of the q…
We briefly discuss constraints on supersymmetric hybrid inflation models and examine the consistency of brane inflation models. We then address the implications for inflationary scenarios resulting from the strong constraints on the cosmic (super)string tension imposed from the most recent cosmic microwave background temperature anisotropies data.
We calculate the bispectrum of the gravitational field fluctuations generated during warm inflation, where dissipation of the vacuum potential during inflation is the mechanism for structure formation. The bispectrum is non--zero because of the self--interaction of the scalar field. We compare the predictions with those of standard, or `supercooled', inflationary models, and consider the detectability of these levels of non--Gaussianity in the bispectrum of the cosmic microwave background. We find that the levels of non--Gaussianity for warm and supercooled inflation are comparable, and over--…
Sources of magnetic fields from grand unified theories are studied in the warm inflation regime. A ferromagnetic Savvidy vacuum scenario is presented that yields observationally interesting large scale magnetic fields. As an intermediate step, a general analysis is made of defect production at the onset of warm inflation and monopole constraints are obtained. Many features of this Savvidy vacuum scenario are applicable within a supercooled inflation regime and these points are discussed.
After decades of successful hot big-bang paradigm, Cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present `quasi' de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this Essay we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular …
