ON THE HORIZON HYPOTHESIS IN QUANTUM COSMOLOGY

1996 ◽  
Vol 05 (02) ◽  
pp. 193-208 ◽  
Author(s):  
M.D. POLLOCK
Keyword(s):  
Quantum Cosmology ◽  
Background Radiation ◽  
Physical Space ◽  
Density Fluctuations ◽  
Hermite Functions ◽  
Parabolic Cylinder ◽  
Microwave Background ◽  
Superstring Theory ◽  
Microwave Background Radiation ◽  
Parabolic Cylinder Functions

The mini-superspace approximation in quantum cosmology, whereby the space—time is restricted to the Friedmann form ds2=dt2−a2(t)dx2, requires the integrated three-space ∫d3x to be finite, in order that the operator replacements p→−iħ∂/∂q are well defined for the canonically conjugate momenta and coordinates (p, q). We have previously agued that this procedure can be made exact by cutting off the physical space at the causal horizon, so that ∫d3x=1 and a(t0)=(4π/3)1/3ξ−1(t0), where ξ≡d(ln a)/dt is the Hubble parameter and t0 is the present time, assuming dx2 to be flat. A corollary of this horizon hypothesis is that all quantum field theoretical integrals are similarly cut off. It is pointed out that the analysis by Jing and Fang of the two-year results for the COBE DMR observations of the quadrupole anisotropy of the cosmic microwave background radiation substantiates this idea (although the alternative explanation, that there are smaller density fluctuations at larger scales, is not ruled out). Also, the cosmological Schrödinger equation (Wheeler-DeWitt equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory of Gross et al., is shown to be separable only when the physical space is isotropic and conformally flat, and in the approximation that quartic and higher-order terms in ξ are ignorable, and the solution is then expressed in terms of parabolic cylinder functions (Weber-Hermite functions). Finally, the occurrence of large density fluctuations via the indeterminacy relation ΔπξΔξ~ħ is further discussed.

Cosmic Density Fluctuations, Magnetic Fields and Gravitational Waves

1997 ◽  
Vol 12 (15) ◽  
pp. 1069-1076 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Galaxy Formation ◽  
Background Radiation ◽  
Density Fluctuations ◽  
Microwave Background ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Microwave Background Radiation ◽  
Dynamo Mechanism ◽  
Gravitational Wave Background ◽  
The Universe

It has previously been shown, for the heterotic superstring theory including higher-derivative terms ℛ2, how metric fluctuations, sufficient for galaxy formation in the Universe, arise as a consequence of the Heisenberg indeterminacy principle, applied to the dynamical auxiliary coordinate [Formula: see text] and its canonically conjugate momentum πξ, defined from the Friedmann space-time [Formula: see text]. This indeterminacy is distributed amongst the scalar, vector and tensor modes of the metric. Therefore, in addition to the fluctuations δρ/ρ in the matter, and in the cosmic microwave background radiation, there is a magnetic field, whose magnitude is estimated to agree approximately with the phenomenological value B c ~ 10-10 G required for the present-day intergalactic field (in the absence of a dynamo mechanism acting on a primordial field B s ≲ 10-17 G), and also a stochastic gravitational wave background, whose energy density must be bounded by the limit Ω gw ≲ 2.6×10-14h-2≈ 10-13 obtained by Krauss and White from the Sachs–Wolfe effect.

ON THE ORIGIN OF DENSITY FLUCTUATIONS IN THE UNIVERSE

1993 ◽  
Vol 08 (14) ◽  
pp. 1285-1290 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Density Fluctuations ◽  
Microwave Background ◽  
Superstring Theory ◽  
Scale Invariant ◽  
Order Unity ◽  
Microwave Background Radiation ◽  
Axion Decay Constant ◽  
Axion Decay ◽  
The Universe

It has been shown by Harrison that quantum fluctuations of the metric at the Planck era lead to a scale-invariant spectrum of density fluctuations ξ ≡ δρ/ρ at all subsequent times of the expansion of a Friedmann universe, irrespective of whether there is inflation. For the vacuum Einstein theory, ξ is of order unity, and thus is too large. But for the dimensionally reduced, heterotic superstring, ξ ≈ πfα/M P ≈ 6 × 10−4, where M P is the Planck mass and fa ≈ 2 × 10−4M P is the axion decay constant. This result is in approximate agreement with the observations of the temperature fluctuations in the cosmic microwave background radiation by COBE, δT/T ≈ 6 × 10−6, and thus constitutes evidence in favor of the superstring theory.

A GAUGE-INVARIANT FLUID DESCRIPTION OF PRIMORDIAL DENSITY FLUCTUATIONS OF COLLISIONLESS PARTICLES

1991 ◽  
Vol 06 (12) ◽  
pp. 2075-2108 ◽  
Author(s):  
ROBERT K. SCHAEFER
Keyword(s):  
Evolution Equations ◽  
Particle Distribution ◽  
Background Radiation ◽  
Density Fluctuations ◽  
Microwave Background ◽  
Significant Component ◽  
Gauge Invariant ◽  
Simple Set ◽  
Moment Approximation ◽  
Microwave Background Radiation

Formulas are derived for describing the evolution of fluctuations in the density of collisionless particles in the expanding universe using the gauge-invariant fluid description. The formulas use the “gauge-invariant” variables proposed by Bardeen to describe cosmological perturbations. These variables are hydrodynamic in nature and we show the behavior of the equations when the particles have streaming lengths large compared to the scales of interest. We also show how these equations couple gravitationally when other species of matter are present in significant densities. Using the “fourteen moment” approximation for the particle distribution function, we get a simple set of ordinary differential equations which are much easier to use than a direct integration of the Boltzmann equation. This formulation is especially useful when we are considering universes with more than one cosmologically significant component of matter density. An example of a numerical integration of the evolution equations is presented for comparison of this method to other work. A formula for calculating fluctuations in the cosmic microwave background radiation is also given.

ON THE HEISENBERG INDETERMINACY PRINCIPLE AND THE FORMATION OF STRUCTURE IN THE UNIVERSE

1995 ◽  
Vol 10 (07) ◽  
pp. 539-547 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Density Fluctuations ◽  
Internal Space ◽  
Superstring Theory ◽  
Scale Invariant ◽  
Classical Action ◽  
Four Dimensions ◽  
Dimensionless Constant ◽  
Microwave Background Radiation ◽  
The Universe

The Heisenberg indeterminacy principle ΔpaΔqa ~ ħ, relating canonically conjugate variables pa and qa, is quantified for the classical action obtained by the reduction of the ten-dimensional heterotic superstring theory to four dimensions, in the mini-superspace (Friedmann space-time) [Formula: see text]. There are two coordinates, α and [Formula: see text], representing position and velocity, respectively, the canonical momenta being [Formula: see text] and [Formula: see text]. In both cases, the result can be expressed as an indeterminacy in the time, (Δt/t)2. The fluctuations connecting position and velocity decrease with time and are always undetectably small, Δt/t ≲ 10−44. But the fluctuations involving velocity and acceleration increase with time, and are evaluated at the time te of equipartition of radiation and matter in the universe. Translated first into a metric fluctuation [Formula: see text], this is equivalent to a Gaussian, scale-invariant spectrum of density fluctuations of magnitude [Formula: see text], where the dimensionless constant B depends only on the compactification scheme. For a Calabi–Yau internal space, the estimate B ≈ 3 implies that ζ ≈ 2 × 10−4, which is sufficient for the creation of galaxies and in approximate agreement with observations of the anisotropy of the cosmic microwave background radiation by COBE and at Tenerife.

INFLATION FROM THE SUPERSTRING VACUUM

2009 ◽  
Vol 24 (20n21) ◽  
pp. 4021-4037
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Physical Space ◽  
Reduction Process ◽  
Tree Level ◽  
Internal Space ◽  
De Sitter ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Microwave Background Radiation

Quartic higher-derivative gravitational terms in the effective Lagrangian of the heterotic superstring theory renormalize the bare, four-dimensional gravitational coupling [Formula: see text], due to the reduction process [Formula: see text], according to the formula [Formula: see text], where A r and B r are the moduli for the physical space gij(xk) and internal space [Formula: see text], respectively. The Euler characteristic [Formula: see text] is negative for a three-generation Calabi–Yau manifold, and therefore both the additional terms, of tree-level and one-loop origin, produce a decrease in κ-2, which changes sign when κ-2 = 0. The corresponding tree-level critical point is [Formula: see text], if we set [Formula: see text] and λ = 15π2, for compactification onto a torus. Values [Formula: see text] yield the anti-gravity region κ-2 < 0, which is analytically accessible from the normal gravity region κ-2 > 0. The only non-singular, vacuum minimum of the potential [Formula: see text] is located at the point [Formula: see text], where [Formula: see text], the quadratic trace anomaly [Formula: see text] dominates over [Formula: see text], and a phase of de Sitter expansion may occur, as first envisaged by Starobinsky, in approximate agreement with the constraint due to the effect of gravitational waves upon the anisotropy of the cosmic microwave background radiation. There is no non-singular minimum of the potential [Formula: see text].

scholarly journals 2. Anisotropy of the blackbody radiation

1985 ◽  
Vol 19 (1) ◽  
pp. 661-664
Author(s):  
D. T. Wilkinson ◽  
F. Melchiorri
Keyword(s):  
Background Radiation ◽  
Temperature Fluctuations ◽  
Thomson Scattering ◽  
Blackbody Radiation ◽  
Density Fluctuations ◽  
Microwave Background ◽  
Initial Temperature Distribution ◽  
Microwave Background Radiation ◽  
Expansion Of The Universe ◽  
The Universe

The 2.7 K microwave background radiation provides a sensitive probe of the universe in the interesting, but poorly understood, epoch around z ˜ 1000. At this time (age ~ 10 yr) the universe has cooled to T ~ 4000 K, the plasma combines, Thomson scattering ceases, and matter and blackbody radiation decouple. Subsequently, the radiation freely propagates to us, carrying the imprint of temperature fluctuations on the z ~ 1000 surface. The temperature fluctuations could have been caused by primordial density fluctuations, anisotropy in the expansion of the universe, or inhomogeneity in the initial temperature distribution; the z = 1000 surface we see was not causally connected at the time the radiation was released. Interpretation of the anisotropy measurements is complicated by the possibility that the matter may have been reionized (e.g. by massive stars), so the radiation may have been rescattered, possibly as late as z ~ 7.

Cosmological Consequences with Randers Conformal of Finsler space

2007 ◽  
Vol 3 (2) ◽  
pp. 203-211
Author(s):  
Arunesh Pandey ◽  
R K Mishra
Keyword(s):  
Background Radiation ◽  
Finsler Space ◽  
Space Time ◽  
Anisotropic Model ◽  
Microwave Background ◽  
Microwave Background Radiation

In this paper we study an anisotropic model of space – time with Finslerian metric. The observed anisotropy of the microwave background radiation is incorporated in the Finslerian metric of space time.

The experience of employment of the mathematical cartography methods in cosmology

2017 ◽  
Vol 923 (5) ◽  
pp. 7-16
Author(s):  
A.V. Kavrayskiy
Keyword(s):  
Background Radiation ◽  
Three Dimensional ◽  
Spherical Coordinates ◽  
Linear Element ◽  
Microwave Background ◽  
Euclidian Space ◽  
Microwave Background Radiation ◽  
Rectangular Coordinates ◽  
The Universe ◽  
Length Distortion

The experience of mathematical modeling of the 3D-sphere in the 4D-space and projecting it by mathematical cartography methods in the 3D-Euclidian space is presented. The problem is solved by introduction of spherical coordinates for the 3D-sphere and their transformation into the rectangular coordinates, using the mathematical cartography methods. The mathematical relationship for calculating the length distortion mp(s) of the ds linear element when projecting the 3D-sphere from the 4-dimensional Euclidian space into three-dimensional Euclidian space is derived. Numerical examples, containing the modeling of the ds small linear element by spherical coordinates of 3D-sphere, projecting this sphere into the 3D-Euclidian space and length of ds calculating by means of its projection dL and size of distortion mp(s) are solved. Based on the model of the Universe known in cosmology as the 3D-sphere, the hypothesis of connection between distortion mp(s) and the known observed effects Redshift and Microwave Background Radiation is considered.

scholarly journals Revisiting cosmic microwave background radiation using blackbody radiation inversion

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Koustav Konar ◽  
Kingshuk Bose ◽  
R. K. Paul
Keyword(s):  
Temperature Distribution ◽  
Cosmic Microwave Background ◽  
Background Radiation ◽  
Big Bang ◽  
Blackbody Radiation ◽  
Microwave Background ◽  
Background Spectrum ◽  
Microwave Background Radiation ◽  
Mathematical Process

AbstractBlackbody radiation inversion is a mathematical process for the determination of probability distribution of temperature from measured radiated power spectrum. In this paper a simple and stable blackbody radiation inversion is achieved by using an analytical function with three determinable parameters for temperature distribution. This inversion technique is used to invert the blackbody radiation field of the cosmic microwave background, the remnant radiation of the hot big bang, to infer the temperature distribution of the generating medium. The salient features of this distribution are investigated and analysis of this distribution predicts the presence of distortion in the cosmic microwave background spectrum.

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