A baby-universe model of cosmic inflation is analyzed using quantum Darwinism. In this model cosmic inflation can be approximated as Brownian motion of a quantum field, and quantum Darwinism implies that decoherence is the result of quantum Brownian motion of the wave function. The quantum Darwinism approach to decoherence in the baby-universe cosmic-inflation model yields the decoherence times of the baby-universes. The result is the equation relating the baby-universe's decoherence time with the Hubble parameter. A brief discussion of the relation between Darwinism and determinism is provided in the Appendix.
We argue that the emergent spacetime picture admits a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to the dynamical emergence of spacetime while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We show that the cosmic inflation arises as a time-dependent solution of the matrix quantum mechanics describing the dynamical process of Planck energy condensate in vacuum without introducing any inflaton field as well as an {\it ad hoc} inflation poten…
We show that GUT cosmic strings generically form after inflation if a {\it non-inert} symmetry breaks after inflation; they form irrespectively of the inflationary scenario and in both supersymmetric and non-supersymmetric theories.
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.
Inflation in the framework of Einstein-Cartan theory is revisited. Einstein-Cartan theory is a natural extension of the General Relativity, with non-vanishing torsion. The connection on Riemann-Cartan spacetime is only compatible with the cosmological principal for a particular form of torsion. We show this form to also be compatible with gauge invariance principle for a non-Abelian and Abelian gauge fields under a certain deviced minimal coupling procedure. We adopt an Abelian gauge field in the form of "cosmic triad". The dynamical field equations are obtained and shown to sustain cosmic inf…
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.
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.
In this paper, we generalize Jordan-Lee-Preskill, an algorithm for simulating flat-space quantum field theories, to 3+1 dimensional inflationary spacetime. The generalized algorithm contains the encoding treatment, the initial state preparation, the inflation process, and the quantum measurement of cosmological observables at late time. The algorithm is helpful for obtaining predictions of cosmic non-Gaussianities, serving as useful benchmark problems for quantum devices, and checking assumptions made about interacting vacuum in the inflationary perturbation theory. Components of our work also…
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…
According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave - CMB - anisotropy ...) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether a…
We investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.
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.
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…
A modified model of gravity with additional positive and negative powers of the scalar curvature, $R$, in the gravitational action is studied. This is done using the Palatini variational principle. It is demonstrated that using such a model might prove useful to explain both the early time inflation and the late time cosmic acceleration without the need for any form of dark energy.
We investigate cosmological inflationary scenarios from a gravitoelectromagnetic theory. Our work is formulated in the light of a recently introduced geometrical Weyl-Invariant scalar-tensor theory of gravity, where the nature of both the electromagnetic potential and the inflaton field is attributed to the space-time geometry. We obtain a Harrison-Zeldovich power spectrum for quantum fluctuations of the inflaton field. In our model the electromagnetic fields have also a nearly scale invariant power spectrum for a power-law inflation. We found that the the seed magnetic fields have a nearly sc…
Cosmic inflation claims to make the initial conditions of the standard big bang "generic". But Boltzmann taught us that the thermodynamic arrow of time arises from very non-generic ("low entropy") initial conditions. I discuss how to reconcile these perspectives. The resulting insights give an interesting way to understand inflation and also compare inflation with other ideas that claim to offer alternative theories of initial conditions.
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.
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…
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 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 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.
We consider the coupling of racetrack inflation to matter fields as realised in the D3/D7 brane system. In particular, we investigate the possibility of cosmic string formation in this system. We find that string formation before or at the onset of racetrack inflation is possible, but they are then inflated away. Furthermore, string formation at the end of inflation is prevented by the presence of the moduli sector. As a consequence, no strings survive racetrack inflation.
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 …
These notes present a brief introduction to Hot Big Bang cosmology and Cosmic Inflation, together with a selection of some recent attempts to embed inflation into string theory. They provide a partial description of lectures presented in courses at Dubrovnik in August 2006, at CERN in January 2007 and at Cargese in August 2007. They are aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or of string theory.
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…
I review the current status of the theory of Cosmic Inflation. My discussion covers the motivation and implementation of the idea, as well as an analysis of recent successes and open questions. There is a special discussion of the physics of ``cosmic coherence'' in the primordial perturbations. The issue of coherence is at the heart of much of the success inflation theory has achieved at the hands of the new microwave background data. While much of this review should be useful to anyone seeking to update their knowledge of inflation theory, I have also made a point of including basic material …
We study the phenomena of mass inflation using the Ori model for a rotating BTZ black hole that is sufficiently far from extremality, and show that the right Cauchy horizon ($\mathcal{CH}^+_R$) of the BTZ black hole becomes singular. Motivated by the recent analysis of Dias, Reall, Santos [J. High Energy Phys. 12 (2019) 097], we choose the retrograde quasinormal modes to govern the decay of perturbations exterior to the black hole. The resulting model captures the violation of the strong cosmic censorship conjecture near extremality. On the other hand, far from extremality, the $\mathcal{CH}^+…
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.
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 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 the context of SUSY GUTs, GUT scale cosmic strings formed at the end of hybrid inflation are compatible with currently available CMB measurements. The maximum allowed cosmic strings contribution to the CMB data constrains the free parameters (mass scales, couplings) of inflationary models. For F-term inflation either the superpotential coupling must be fine tuned or one has to invoke the curvaton mechanism. D-term inflation should be addressed in the framework of SUGRA. We find that the cosmic strings contribution is not constant, contrary to some previous results. Using CMB measurements we…
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.
There have been long debates about the initial condition of inflationary perturbations. In this work we explicitly show the decay of excited states during inflation via interactions. For this purpose, we note that the folded shape non-Gaussianity can be interpreted as the decay of the non-Bunch-Davies initial condition. The one loop diagrams with non-Bunch-Davies propagators are calculated to uncover the decay of such excited states. The observed smallness of non-Gaussianity keeps the window open for probing inflationary initial conditions and trans-Planckian physics.
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…
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…
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 …
Recent BICEP2 detection of low-multipole B-mode polarization anisotropy in the cosmic microwave background radiation supports the inflationary universe scenario and suggests a large inflaton field range. The latter feature can be achieved with axion fields in the framework of string theory. We present such a helical model which naturally becomes a model with a single cosine potential, and which in turn reduces to the (quadratic) chaotic inflation model in the super-Planckian limit. The slightly smaller tensor/scalar ratio $r$ of models of this type provides a signature of the periodic nature o…
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.
We investigate the longitudinal ghost issue in Abelian vector inflation. It turns out that, within the class of Lorentz-invariant vector field theories with three degrees of freedom and without any extra (scalar) fields, the possibilities are essentially exhausted by the classical solution due to Larry Ford with an extremely flat potential which doesn't feel the fast roll of its argument. And, moreover, one needs to fulfil an extra condition on that potential in order to avoid severe gradient instability. At the same time, some Lorentz-violating modifications are worth to be explored.
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…
In this work we study the imprints of a primordial cosmic string on inflationary power spectrum. Cosmic string induces two distinct contributions on curvature perturbations power spectrum. The first type of correction respects the translation invariance while violating isotropy. This generates quadrupolar statistical anisotropy in CMB maps which is constrained by the Planck data. The second contribution breaks both homogeneity and isotropy, generating a dipolar power asymmetry in variance of temperature fluctuations with its amplitude falling on small scales. We show that the strongest constra…
We show that holographic dark energy could explain why the current dark energy density is so small, if there was an inflation with a sufficient expansion in the early universe. It is also suggested that an inflation with the number of e-folds $N\simeq 65$ may solve the cosmic coincidence problem in this context. Assuming the inflation and the power-law acceleration phase today we obtain approximate formulas for the event horizon size of the universe and dark energy density as functions of time. A simple numerical study exploiting the formula well reproduces the observed evolution of dark energ…
We present a superstring-inspired version of D-term inflation which does not lead to cosmic string formation and appears to satisfy the current CMB constraints. It differs from minimal D-term inflation by a second pair of charged superfields which makes the strings non-topological (semilocal). The strings are also BPS, so the scenario is expected to survive supergravity corrections. The second pair of charged superfields arises naturally in several brane and conifold scenarios, but its effect on cosmic string formation had not been noticed so far.
We study cosmic string formation within supersymmetric grand unified theories. We consider gauge groups having a rank between 4 and 8. We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem, lead to baryogenesis after inflation and are consistent with proton lifetime measurements. We conclude that in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. The strings which form at the end of infl…
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 curl (B) modes of cosmic microwave background (CMB) polarization anisotropies are a unique probe of the primordial background of inflationary gravitational waves (IGWs). Unfortunately, the B-mode polarization anisotropies generated by gravitational waves at recombination are confused with those generated by the mixing of gradient-mode (E-mode) and B-mode polarization anisotropies as CMB photons propagate through the Universe and are gravitationally lensed. We describe here a method for delensing CMB polarization anisotropies using observations of anisotropies in the cosmic 21-cm radiation …
Overall, brane inflation is compatible with the recent analysis of the WMAP data. Here we explore the constraints of WMAP and 2dFGRS data on the various brane inflationary scenarios. Brane inflation naturally ends with the production of cosmic strings, which may provide a way to distinguish these models observationally. We argue that currently available data cannot exclude a non-negligible contribution from cosmic strings definitively. We perform a partial statistical analysis of mixed models that include a sub-dominant contribution from cosmic strings. Although the data favor models without c…
D-term inflation is one of the most interesting and versatile models of inflation. It is possible to implement naturally D-term inflation within high energy physics, as for example SUSY GUTs, SUGRA, or string theories. D-term inflation avoids the $η$-problem, while in its standard form it always ends with the formation of cosmic strings. Given the recent three-year WMAP data on the cosmic microwave background temperature anisotropies, we examine whether D-term inflation can be successfully implemented in non-minimal supergravity theories. We show that for all our choices of Kähler potential, t…
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…
