On the new string theory inspired mechanism of generation of cosmological perturbations

Recently a non-inflationary mechanism of generation of scale-free cosmological perturbations of metric was proposed by Brandenberger, Nayeri, and Vafa in the context of the string gas cosmology. We discuss various problems of their model and argue that the cosmological perturbations of metric produced in this model have blue spectrum with a spectral index n = 5, which strongly disagrees with observations. We conclude that this model in its present form is not a viable alternative to inflationary cosmology.Comment: 11 pages, 1 figur

Observational Constraints on Theories with a Blue Spectrum of Tensor Modes

Motivated by the string gas cosmological model, which predicts a blue tilt of the primordial gravitational wave spectrum, we examine the constraints imposed by current and planned observations on a blue tilted tensor spectrum. Starting from an expression for the primordial gravitational wave spectrum normalized using cosmic microwave background observations, pulsar timing, direct detection and nucleosynthesis bounds are examined. If we assume a tensor to scalar ratio on scales of the CMB which equals the current observational upper bound, we obtain from these current observations constraints on the tensor spectral index of $n_{T} \lesssim 0.79$, $n_{T} \lesssim 0.53$, and $n_{T} \lesssim 0.15$ respectively.Comment: 12 pages, 1 figure, 2 references added, relationship of this work with Ref. 20 adde

Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.Comment: 4 pages, 1 figur

Cosmological Perturbations in Non-Commutative Inflation

We compute the spectrum of cosmological perturbations in a scenario in which inflation is driven by radiation in a non-commutative space-time. In this scenario, the non-commutativity of space and time leads to a modified dispersion relation for radiation with two branches, which allows for inflation. The initial conditions for the cosmological fluctuations are thermal. This is to be contrasted with the situation in models of inflation in which the accelerated expansion of space is driven by the potential energy of a scalar field, and in which the fluctuations are of quantum vacuum type. We find that, in the limit that the expansion of space is almost exponential, the spectrum of fluctuations is scale-invariant with a slight red tilt. The magnitude of the tilt is different from what is obtained in a usual inflationary model with the same expansion rate during the period of inflation. The amplitude also differs, and can easily be adjusted to agree with observations.Comment: 7 pages, 1 figur

Inaccessible Singularities in Toral Cosmology

The familiar Bang/Crunch singularities of classical cosmology have recently been augmented by new varieties: rips, sudden singularities, and so on. These tend to be associated with final states. Here we consider an alternative possibility for the initial state: a singularity which has the novel property of being inaccessible to physically well-defined probes. These singularities arise naturally in cosmologies with toral spatial sections.Comment: 10 pages, version to appear in Classical and Quantum Gravit

Near Scale Invariance with Modified Dispersion Relations

We describe a novel mechanism to seed a nearly scale invariant spectrum of adiabatic perturbations during a non-inflationary stage. It relies on a modified dispersion relation that contains higher powers of the spatial momentum of matter perturbations. We implement this idea in the context of a massless scalar field in an otherwise perfectly homogeneous universe. The couplings of the field to background scalars and tensors give rise to the required modification of its dispersion relation, and the couplings of the scalar to matter result in an adiabatic primordial spectrum. This work is meant to explicitly illustrate that it is possible to seed nearly scale invariant primordial spectra without inflation, within a conventional expansion history.Comment: 7 pages and no figures. Uses RevTeX

Lectures on Cosmic Inflation and its Potential Stringy Realizations

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.Comment: 68 pages, lectures given at Dubrovnik, Aug 2006; CERN, January 2007; and Cargese, Aug 200

Fractional Brane State in the Early Universe

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap around the cycles of the torus. We find an equation of state p_i=w_i rho, for which the dynamics can be solved analytically. For black holes, fractionation can lead to non-local quantum gravity effects across length scales of order the horizon radius; similar effects in the early Universe might change our understanding of Cosmology in basic ways.Comment: 40 pages, 18 figures, references adde

Non-perturbative gravity, Hagedorn bounce and the cosmic microwave background.

In Biswas et al (2006 J. Cosmol. Astropart. Phys. JCAP03(2006)009 [hep-th/0508194]) it was shown how non-perturbative corrections to gravity can resolve the big bang singularity, leading to a bouncing universe. Depending on the scale of the non-perturbative corrections, the temperature at the bounce may be close to or higher than the Hagedorn temperature. If matter is made up of strings, then massive string states will be excited near the bounce, and the bounce will occur inside (or at the onset of) the Hagedorn phase for string matter. As we discuss in this paper, in this case cosmological fluctuations can be generated via the string gas mechanism recently proposed in Nayeri et al (2005 Preprint hep-th/0511140). In fact, the model discussed here demonstrates explicitly that it is possible to realize the assumptions made in Nayeri et al (2005 Preprint hep-th/0511140) in the context of a concrete set of dynamical background equations. We also calculate the spectral tilt of thermodynamic stringy fluctuations generated in the Hagedorn regime in this bouncing universe scenario. Generally we find a scale-invariant spectrum with a red tilt which is very small but does not vanish