In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and the quantum theory is characterized by finite dimensional Hilbert space. Furthermore, by considering the $\mathbb{S}^2$ phase space, quantum description is constructed with the use $SU(2)$ representation theory. The purpose of this article is to apply effective methods to extract semi-classical regime of the quantum dynamics. The analysis is performed both without prior solving of the quantum constraint and by extracting physical Hamiltonian of the model. At the effective level, the results of the two procedures are shown to be equivalent. We find a nontrivial behavior of the fluctuations around the recollapse of the universe, which is distinct from what is found after quantization with the standard flat phase space. The behavior is reflected at the level of the modified Friedmann equation with quantum back-reaction effects, which is derived. Finally, an unexpected relation between the quantum fluctuations of the cosmological sector and the holographic Bousso bound is shown.
Quantum fluctuations or other moments of a state contribute to energy expectation values and can imply interesting physical effects. In quantum cosmology, they turn out to be important for a discussion of density bounds and instabilities of initial-value problems in the presence of signature change in loop-quantized models. This article provides an effective description of these issues, accompanied by a comparison with existing numerical results and an extension to squeezed states. The comparison confirms that canonical effective methods are well-suited for computations of properties of physic…
In this note, we revisit the thermal fluctuations generated during bouncing cosmology, taking Unruh effect into account. We find that due to the additional effect on temperature, the dependence of power spectrum on $k$ will get corrected with an indication of blue tilt at large $k$ region, which is in consistent with the case of vacuum initial conditions.
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of the matter clock observables, to test the validity of the relational evolution picture itself. Next, we compute quantum fluctuations of the universe volume and of other operators characterizing its evolution (number operator for the fundamental GFT quanta, effective Hamiltonian and scalar field momentum). In particular, we focus on the late (clock) time regim…
The Wheeler-De Witt equation of type IIB quantum string cosmology compactified with constant internal H-fluxes on a 6-torus, whose volume modulus is frozen, is solved under the WKB approximation. The spontaneous symmetry breaking of the S-duality group by H-fluxes is also examined.
Fluctuations on de Sitter solution of Einstein-Cartan field equations are obtained in terms of the matter density primordial density fluctuations and spin-torsion density and matter density fluctuations obtained from COBE data. Einstein-de Sitter solution is shown to be unstable even in the absence of torsion.The spin-torsion density fluctuation to generate a deflationary phase is computed from the COBE data.
We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wron…
We solve exactly the (linear order) equations for tensor and scalar perturbations over the homogeneous, isotropic, open pre-big bang model recently discussed by several authors. We find that the parametric amplification of vacuum fluctuations (i.e. particle production) remains negligible throughout the perturbative pre-big bang phase.
This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid expansion can stretch microscopic fluctuations to cosmological proportions. I discuss also another important conseqence of quantum fluctuations: the fact that almost all inflationary models become eternal, so that once inflation starts, it never stops.
In this paper we investigate the power spectrum of thermal fluctuations in very early stage of viscous cosmology. When the state parameter as well as the viscous coefficient of a barotropic fluid is properly chosen, a scale invariant spectrum with large non-Gaussianity can be obtained. In contrast to the results previously obtained in string gas cosmology and holographic cosmology, we find the non-Gaussianity in this context can be k-independent such that it is not suppressed at large scale, which is expected to be testified in future observation.
The notion of vacuum fluctuations of the gravitational field plays important role in cosmology. The strong variable gravitational field of the very early Universe amplifies these fluctuations and transforms them into macroscopical cosmological perturbations. Since the underlying process is the parametric amplification, the perturbations are placed in squeezed vacuum quantum states. It is possible that we already see the manifestations of these processes in certain cosmological observations.
We study cosmological perturbations arising from thermal fluctuations in the big-bounce cosmology in the Einstein-Cartan-Sciama-Kibble theory of gravity. We show that such perturbations cannot have a scale-invariant spectrum if fermionic matter minimally coupled to the torsion tensor is macroscopically averaged as a spin fluid, but have a scale-invariant spectrum if the Dirac form of the spin tensor of the fermionic matter is used.
A calculation of the one-mode occupation numbers for vacuum fluctuations of massive fields in De Sitter space shows that their use for the generation of classical density perturbations in inflationary cosmology very much depends on their masses and conformal couplings. A new mechanism for the decoherence of relatively massive fields has been identified. A similar analysis of the power law inflation shows that production of adiabatic density perturbations may not take place in models with power p < 3.
Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider loop modifications to the behavior of the inverse scale factor below a critical scale in closed models and assume a purely thermal origin for the fluctuations. We show that the no-go results for scale invariance in classical thermal models can be evaded even if we just consider modifications to the background (zeroth order) gravitational dynamics. Since a com…
We calculate the power spectrum of vacuum fluctuations of a generic scalar field in a quantum cosmological setting that is manifestly singularity-free. The power spectrum is given in terms of the usual scale invariant spectrum plus scale dependent corrections. These are induced by well-defined quantum fluctuations of de Sitter spacetime, resulting in a modified dispersion relation for the scalar field. The leading correction turns out to be proportional to the ratio of Hubble scale and Planck Mass. The maximal relative change in the spectrum is on the ten percent level and might be observable …
We review several related investigations of the effects of the quantum stress tensor of a conformal field in inflationary cosmology. Particular attention will be paid to the effects of quantum stress tensor fluctuations as a source of density and tensor perturbations in inflationary models. These effects can possibly depend upon the total expansion factor during inflation, and hence be much larger than one might otherwise expect. They have the potential to contribute a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations, and might be observable.
We analyse the spectrum of energy density fluctuations of a dual supergravity model where the dilaton and the moduli are stabilized and sucessful inflation is achieved inside domain walls that separate different vacua of the theory. Constraints on the parameters of the superpotential are derived from the amplitude of the primordial energy density fluctuations as inferred from COBE and it is shown that the scale dependence of the tensor perturbations nearly vanishes.
We give a short update of our research program on nonequilibrium statistical field theory applied to quantum processes in the early universe and black holes, as well as the development of stochastic gravity theory as an extension of semiclassical gravity and an intermediary in the 'bottom-up' approach to quantum gravity.
An analysis of the decoherence of quantum fluctuations shows that production of classical adiabatic density perturbations may not take place in models of power-law inflation with power 1< p < 3. Some consequences for models of extended inflation are pointed out. In general, the condition for decoherence places new constraint on inflationary models, which does not depend on often complicated subsequent evolution.
It is shown how quantum fluctuations of the radiation during the contraction era of a CBE (Comes Back Empty) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel'dovich-Peebles sense, as necessary to be consistent with observations of large scale structure.
It is shown that density fluctuations obey a scaling law in an open Friedmann universe. In a flat universe, the fluctuations are not scale-invariant. We compute the growth rate of adiabatic scale-invariant density fluctuations in flat, open and inflationary universes. We find that, given a sufficiently long time, the density perturbations decay away in the Einstein-de-Sitter universe. On the contrary, the rapid growth of the density instabilities makes an open universe inhomogeneous in a time scale comparable to the age of our universe. We also find that the fluctuations grow exponentially in …
We study the evolution of fluctuations in a universe dominated by a scalar field coupled to the Gauss-Bonnet term. During the graceful exit, we found non-negligible enhancements of both curvature perturbation and gravitational wave in the long wavelength limit, and we also found a short wavelength instability for steep background superinflation just after the completion of the graceful exit. This result for one possible graceful exit mechanism would provide a significant implication on the primordial spectrum from the string cos mology.
We suggest a new conceptual frame where inflationary Cosmology is quantum mechanically described using the Hilbert space representation of the crossed product of the type $III$ factor associated with the algebra of local operators on the de Sitter static patch and the automorphism of translations in the emergent conformal time. In this formal framework scalar curvature fluctuations are determined by the gravitational potential induced by the quantum variance of the generator of the conformal time automorphisms. Choosing as representative, in the Hilbert space of the crossed product, the effect…
Primordial fluctuations in inflationary cosmology acquire classical properties through decoherence when their wavelengths become larger than the Hubble scale. Although decoherence is effective, it is not complete, so a significant part of primordial correlations remains up to the present moment. We address the issue of the pointer states which provide a classical basis for the fluctuations with respect to the influence by an environment (other fields). Applying methods from the quantum theory of open systems (the Lindblad equation), we show that this basis is given by narrow Gaussians that app…
We calculate the power spectrum of metric fluctuations in inflationary cosmology starting with initial conditions which are imposed mode by mode when the wavelength equals some critical length $\ell_{_{\rm C}}$ corresponding to a new energy scale $M_{_{\rm C}}$ at which trans-Planckian physics becomes important. In this case, the power spectrum can differ from what is calculated in the usual framework (which amounts to choosing the adiabatic vacuum state). The fractional difference in the results depends on the ratio $σ_0$ between the Hubble expansion rate $H_{\rm inf}$ during inflation and th…
A variable speed of light (VSL) cosmology is described in which the causal mechanism of generating primordial perturbations is achieved by varying the speed of light in a primordial epoch. This yields an alternative to inflation for explaining the formation of the cosmic microwave background (CMB) and the large scale structure (LSS) of the universe. The initial value horizon and flatness problems in cosmology are solved. The model predicts primordial scalar and tensor fluctuation spectral indices $n_s=0.96$ and $n_t=- 0.04$, respectively. We make use of the $δ{\cal N}$ formalism to identify si…
Hořava-Lifshitz gravity is a potentially UV complete theory with important implications for the very early universe. In particular, in the presence of spatial curvature it is possible to obtain a non-singular bouncing cosmology. The bounce is realized as a consequence of higher order spatial curvature terms in the gravitational action. Here, we extend the study of linear cosmological perturbations in Hořava-Lifshitz gravity coupled to matter in the case when spatial curvature is present. As in the case without spatial curvature, we find that there is no extra dynamical degree of freedom for sc…
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.
Inflationary string cosmology backgrounds can amplify perturbations in a more efficient way than conventional inflationary backgrounds, because the perturbation amplitude may grow - instead of being constant - outside the horizon. If not gauged away, the growing mode can limit the range of validity of a linearized description of perturbations. Even in the restricted linear range, however, this enhanced amplification may lead to phenomenological consequences unexpected in the context of the standard inflationary scenario. In particular, the production of a relic graviton background strong enoug…
We review the successes and challenges of the holographic approach to cosmology. The model predicts an exactly scale invariant fluctuation spectrum with long and short distance cut-offs. It can account for the observed fluctuations in the CMB and might explain the low power at large scales. We outline various cosmological histories compatible with holographic initial conditions. This paper is based on talks given by the authors at Cosmo 04 in Toronto, and the 2004 Tamura Symposium in Austin
We discuss bounds on the dilaton mass, following from the cosmological amplification of the quantum fluctuations of the dilaton background, under the assumption that such fluctuations are dominant with respect to the classical background oscillations. We show that if the fluctuation spectrum grows with the frequency the bounds are relaxed with respect to the more conventional case of a flat or decreasing spectrum. As a consequence, the allowed range of masses may become compatible with models of supersymmetry breaking, and with a universe presently dominated by a relic background of dilaton da…
Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is achieved for a special class of perfect fluids. The external space behaves in accordance with the standard Friedmann model. Necessary restrictions on the parameters of the models are found to ensure dynamical behavior of the external (our) universe in agreement with observations.
Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise dynamical coherent states and their evolution in such a setting. It is shown here that quantum fluctuations before the big bang are generically unrelated to those after the big bang. A reliable determination of pre-big bang quantum fluctuations would require exceedingly precise observations.
We set constraints on moduli cosmology from the production of dark matter -- radiation and baryon -- radiation isocurvature fluctuations through modulus decay, assuming the modulus remains light during inflation. We find that the moduli problem becomes worse at the perturbative level as a significant part of the parameter space m_σ(modulus mass) -- σ_{inf} (modulus vev at the end of inflation) is constrained by the non-observation of significant isocurvature fluctuations. We discuss in detail the evolution of the modulus vev and perturbations, in particular the consequences of Hubble scale cor…
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the negative part of the spectrum of the Hamiltonian that generates this evolution. It is shown here that the restricted support on the spectrum does not significantly limit the possible values of volume fluctuations.
In this contribution to the proceedings of the Conference on Modern Physics of Compact Stars and Relativistic Gravity in Yerevan, Armenia (September 18-21, 2013), I review recent work attempting to give a fundamental definition to string evolution in a dynamical, fully compact universe, and present a sketch of how the resulting formalism can be used for addressing questions of phenomenological significance in the field of string gas cosmology.
We study the classical and quantum cosmology of a 4+1-dimensional space-time with a non-zero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor $R(t)$ and an internal scale factor $a(t)$ associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition fr…
A model universe is proposed in the framework of 5-dimensional noncompact Kaluza-Klein cosmology which is not Ricci flat. The 4D part as the Robertson-Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the non-vacuum states of the scalar field would contribute to 4D cosmology.
We reconsider theories with low gravitational (or string) scale M_* where Newton's constant is generated via new large-volume spatial dimensions, while Standard Model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds (CHM's) we show that the spectrum of Kaluza-Klein (KK) modes is radically altered. This allows an early universe cosmology with normal evolution up to substantial temperatures, and completely negates the constraints on M_* arising from astrophysics. Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physic…
This thesis is dedicated to the study of inflationary scenarios based on string theory. Inflation is a brief period of accelerated expansion in the very early Universe which gives natural explanations for problems of the Standard Big Bang Model (SBBM) of cosmology. The phenomenological success of inflation provides the motivation for numerous efforts to establish its connection with particle physics. As a promising contender for a unified theory at very high energy scales, string theory is an obvious framework to look for the theoretical foundations of inflation; we therefore try to determine …
Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.
We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly sc…
We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l=constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the $l\simeq0$ constant hypersurface.
In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space $\mathbb{M}_2$, it is possible to obtain a variety of inhomogeneous metrics in $\mathbb{M}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant $Λ_4$, and in particular, it is possible to obtain $Λ_4 =0$, as is confirmed by nu…
We calculate the expected angular power spectrum of the temperature fluctuations in the microwave background radiation (MBR) generated in the quasi-steady state cosmology (QSSC). The paper begins with a brief description of how the background is produced and thermalized in the QSSC. We then discuss within the framework of a simple model, the likely sources of fluctuations in the background due to astrophysical and cosmological causes. Power spectrum peaks at $l \approx 6-10$, 180-220 and 600-900 are shown to be related in this cosmology respectively to curvature effects at the last minimum of …
We discuss the appearance of time-asymmetric behavior in physical processes in cosmology and in the dynamics of the Universe itself. We begin with an analysis of the nature and origin of irreversibility in well-known physical processes such as dispersion, diffusion, dissipation and mixing, and make the distinction between processes whose irreversibility arises from the stipulation of special initial conditions, and those arising from the system's interaction with a coarse-grained environment. We then study the irreversibility associated with quantum fluctuations in cosmological processes like …
We study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic non-inflationary bouncing cosmology, pertur…
We consider an inflationary universe model in which the phase of accelerated expansion was preceded by a non-singular bounce and a period of contraction which involves a phase of deceleration. We follow fluctuations which exit the Hubble radius in the radiation-dominated contracting phase as quantum vacuum fluctuations, re-enter the Hubble radius in the deflationary period and re-cross during the phase of inflationary expansion. Evolving the fluctuations using the general relativistic linear perturbation equations, we find that they exit the Hubble radius during inflation not with a scale-inva…
We study on the third quantization of a Kaluza-Klein toy model. In this model time ($x$) is defined by the scale factor of universe, and the space coordinate ($y$) is defined by the ratio of the scales of the ordinary space and the internal space. We calculate the number density of the universes created from nothing and examine whether the compactification can be explained statistically by the idea of the third quantization.
We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic stat…
We present a cosmological model in 1+m+p dimensions, where in m-dimensional space there are uniformly distributed p-branes wrapping over the extra p-dimensions. We find that during cosmological evolution m-dimensional space expands with the exact power-law corresponding to pressureless matter while the extra p-dimensions contract. Adding matter, we also obtain solutions having the same property. We show that this might explain in a natural way why the extra dimensions are small compared to the observed three spatial directions.
We investigate Holographic Dark Energy Correspondence of Interacting Generalized Chaplygin Gas model in the framework of compact Kaluza-Klein cosmology. The evolution of the modified holographic dark energy and the equation of state parameter is obtained here.Using the present observational value of density parameter a stable configuration is formed which accommodates Dark Energy. we note a connection between Dark Energy and Phantom field and have shown that Dark Energy might have evolved from a Phantom state in the past.
String Gas Cosmology is a model of the evolution of the very early universe based on fundamental principles and key new degrees of freedom of string theory which are different from those of point particle field theories. In String Gas Cosmology the universe starts in a quasi-static Hagedorn phase during which space is filled with a gas of highly excited string states. Thermal fluctuations of this string gas lead to an almost scale-invariant spectrum of curvature fluctuations. Thus, String Gas Cosmology is an alternative to cosmological inflation as a theory for the origin of structure in the u…
We address two basic issues in the theory of galaxy formation from fluctuations of quantum fields: 1) the nature and origin of noise and fluctuations and 2) the conditions for using a classical stochastic equation for their description. On the first issue, we derive the influence functional for a $λϕ^4 $ field in a zero-temperature bath in de Sitter universe and obtain the correlator for the colored noises of vacuum fluctuations. This exemplifies a new mechanism we propose for colored noise generation which can act as seeds for galaxy formation with non-Gaussian distributions. For the second i…
Small fluctuations around homogeneous and isotropic expanding backgrounds are the main object of study in cosmology. Their origin and evolution is sensitive to the physical processes that happen during inflation and in the late Universe. As such, they hold the key to answering many of the major open questions in cosmology. Given a large separation of relevant scales in many examples of interest, the most natural description of these fluctuations is formulated in terms of effective field theories. This was the main avenue for many of the important modern developments in theoretical cosmology, w…
Using the concept of open systems where the classical geometry is treated as the system and the quantum matter field as the environment, we derive a fluctuation-dissipation theorem for semiclassical cosmology. This theorem which exists under very general conditions for dissipations in the dynamics of the system, and the noise and fluctuations in the environment, can be traced to the formal mathematical relation between the dissipation and noise kernels of the influence functional depicting the open system, and is ultimately a consequence of the unitarity of the closed system. In particular, fo…
We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices, and the tensor to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be…
