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.

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.

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.

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.

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.

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.

The TopHat Cosmic Microwave Background Anisotropy Experiment

2005 ◽  
Vol 201 ◽  
pp. 65-70
Author(s):  
Robert F. Silverberg ◽  
Keyword(s):  
Cosmic Microwave Background ◽  
Large Scale ◽  
Background Radiation ◽  
High Sensitivity ◽  
Microwave Background ◽  
Long Duration ◽  
Cosmic Microwave Background Anisotropy ◽  
Microwave Background Radiation ◽  
The Universe ◽  
Large Scale Structure Formation

We have developed a balloon-borne experiment to measure the Cosmic Microwave Background Radiation anisotropy on angular scales from ˜50° down to ˜20′. The instrument observes at frequencies between 150 and 690 GHz and will be flown on an Antarctic circumpolar long duration flight. To greatly improve the experiment performance, the front-end of the experiment is mounted on the top of the balloon. With high sensitivity, broad sky coverage, and well-characterized systematic errors, the results of this experiment can be used to strongly constrain cosmological models and probe the early stages of large-scale structure formation in the Universe.

scholarly journals The question on origin of the universe and Big Bang

2011 ◽  
Vol 2 ◽  
pp. 67-70
Author(s):  
Krishna Raj Adhikari
Keyword(s):  
Cosmic Microwave Background ◽  
Background Radiation ◽  
Scientific Evidence ◽  
Big Bang ◽  
Cosmic Microwave Background Radiation ◽  
Microwave Background ◽  
Microwave Background Radiation ◽  
Physics Department ◽  
The Universe ◽  
Origin Of The Universe

School of thought is the theory of creation (theism) and school of thought deals with the random chance of evolution (atheism) about the origin of the universe and origin of the life. In the race of proof of the hypothesis, the theism has no scientific evidence and reliable proof, on the other hand atheism based on the scientific observable evidence. The latest theory of origin of the universe by Big Bang is more believable and supported by some scientific evidence such as Doppler effect on light, Hubble observation and result of the expanding the universe and observation of the cosmic microwave background radiation(CMBR). Paper briefly discussing about the origin of the universe and the Bing Bang.Key words: Big bang; Doppler; Cosmic microwave background radiation(CMBR)The Himalayan Physics Department of Physics, PN Campus, Pokhara Nepal Physical Society, Western Regional ChapterVol.2, No.2, May, 2011Page: 67-70Uploaded Date: 1 August, 2011

scholarly journals Testing theories of gravity and supergravity with inflation and observations of the cosmic microwave background

2017 ◽  
Vol 26 (13) ◽  
pp. 1730023 ◽  
Author(s):  
G. K. Chakravarty ◽  
S. Mohanty ◽  
G. Lambiase
Keyword(s):  
General Relativity ◽  
Cosmic Microwave Background ◽  
Cold Dark Matter ◽  
Background Radiation ◽  
Accelerated Expansion ◽  
Microwave Background ◽  
Microwave Background Radiation ◽  
Theories Of Gravity ◽  
The Universe ◽  
Einstein’S General Relativity

Cosmological and astrophysical observations lead to the emerging picture of a universe that is spatially flat and presently undertaking an accelerated expansion. The observations supporting this picture come from a range of measurements encompassing estimates of galaxy cluster masses, the Hubble diagram derived from type-Ia supernovae observations, the measurements of Cosmic Microwave Background radiation anisotropies, etc. The present accelerated expansion of the universe can be explained by admitting the existence of a cosmic fluid, with negative pressure. In the simplest scenario, this unknown component of the universe, the Dark Energy, is represented by the cosmological constant ([Formula: see text]), and accounts for about 70% of the global energy budget of the universe. The remaining 30% consist of a small fraction of baryons (4%) with the rest being Cold Dark Matter (CDM). The Lambda Cold Dark Matter ([Formula: see text]CDM) model, i.e. General Relativity with cosmological constant, is in good agreement with observations. It can be assumed as the first step towards a new standard cosmological model. However, despite the satisfying agreement with observations, the [Formula: see text]CDM model presents lack of congruence and shortcomings and therefore theories beyond Einstein’s General Relativity are called for. Many extensions of Einstein’s theory of gravity have been studied and proposed with various motivations like the quest for a quantum theory of gravity to extensions of anomalies in observations at the solar system, galactic and cosmological scales. These extensions include adding higher powers of Ricci curvature [Formula: see text], coupling the Ricci curvature with scalar fields and generalized functions of [Formula: see text]. In addition, when viewed from the perspective of Supergravity (SUGRA), many of these theories may originate from the same SUGRA theory, but interpreted in different frames. SUGRA therefore serves as a good framework for organizing and generalizing theories of gravity beyond General Relativity. All these theories when applied to inflation (a rapid expansion of early universe in which primordial gravitational waves might be generated and might still be detectable by the imprint they left or by the ripples that persist today) can have distinct signatures in the Cosmic Microwave Background radiation temperature and polarization anisotropies. We give a review of [Formula: see text]CDM cosmology and survey the theories of gravity beyond Einstein’s General Relativity, specially which arise from SUGRA, and study the consequences of these theories in the context of inflation and put bounds on the theories and the parameters therein from the observational experiments like PLANCK, Keck/BICEP, etc. The possibility of testing these theories in the near future in CMB observations and new data coming from colliders like the LHC, provides an unique opportunity for constructing verifiable models of particle physics and General Relativity.

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