Inflationary predictions for scalar and tensor fluctuations reconsidered

Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum P ( k ) and the CMB temperature angular power spectrum C l ’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients C l , which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.

Can the Inflaton Also Be a Weakly Interacting Massive Particle?

We propose a class of models in which a stable inflaton is produced as a thermal relic in the early Universe and constitutes the dark matter. We show that inflaton annihilations can efficiently reheat the Universe, and identify several examples of inflationary potentials that can accommodate all cosmic microwave background observables and in which the inflaton dark matter candidate has a weak scale mass. As a simple example, we consider annihilations that take place through a Higgs portal interaction, leading to encouraging prospects for future direct detection experiments.

Gravitational Fluctuations as an Alternative to Inflation

The ability to reproduce the observed matter power spectrum P ( k ) to high accuracy is often considered as a triumph of inflation. In this work, we explore an alternative explanation for the power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of ones based on inflation models. In particular, the power spectral index, which governs the slope on the P ( k ) graph, can be related to critical scaling exponents derived from the Wilson renormalization group analysis. We find that the derived value fits favorably with the Sloan Digital Sky Survey telescope data. We then make use of the transfer functions, based only on the Boltzmann equations, which describe states out of equilibrium, and Einstein’s general relativity, to extrapolate the power spectrum to the Cosmic Microwave Background (CMB) regime. We observe that the results fit rather well with current data. Our approach contrasts with the conventional explanation, which uses inflation to generate the scale-invariant Harrison–Zel’dovich spectrum on CMB scales and uses the transfer function to extrapolate it to the galaxy regime. The results we present here only assume quantum field theory and Einstein’s gravity, and hence provide a competing explanation of the power spectrum, without relying on the assumptions usually associated with inflationary models. At the end, we also outline several testable predictions in this picture that deviate from the conventional picture of inflation and which hopefully will become verifiable in the near future with increasingly accurate measurements.

Generalized Poincaré sphere

We present a generalized Poincaré sphere (G sphere) and generalized Stokes parameters (G parameters), as a geometric representation, which unifies the descriptors of a variety of vector fields. Unlike the standard Poincaré sphere, the radial dimension in the G sphere is not used to describe the partially polarized field. The G sphere is constructed by extending the basic Jones vector bases to the general vector bases with the continuously changeable ellipticity (spin angular momentum, SAM) and the higher dimensional orbital angular momentum (OAM). The north and south poles of different spherical shells in the G sphere represent the pair of different orthogonal vector basis with different ellipticity (SAM) and the opposite OAM. The higher-order Poincaré spheres are just the two special spherical shells of the G sphere. We present a quite flexible scheme, which can generate all the vector fields described in the G sphere.

Precursor of inflation

We investigate a nonsingular initial state of the Universe which leads to inflation naturally. The model is described by a scalar field with a quadratic potential in Eddington-inspired Born-Infeld gravity. The curvature of this initial state is given by the mass scale of the scalar field, which is much smaller than the Planck scale. Therefore, in this model, quantum gravity is not necessary in understanding this preinflationary stage, no matter how large the energy density becomes. The initial state in this model evolves eventually to a long inflationary period which is similar to the usual chaotic inflation.

Testing inflation: a bootstrap approach

We note that the essential idea of inflation, that the Universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion, can be encapsulated in a "closure condition" which relates the amount of accelerated expansion during inflation to the amount of decelerated expansion afterward. We present a protocol for systematically testing the validity of this condition observationally.