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Steven Weinberg

Publications and source records attributed to Steven Weinberg.

At least 55 records · Page 3Linked to original sources
arXiv2002

Cosmological Fluctuations of Short Wavelength

This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for the conventional transfer function T(k) at large wave number k, which agrees very well with computer calculations of T(k). It also yields an explicit formula for the microwave background multipole coefficient C_ell at very large ell.

astro-ph↗
arXiv2001

Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations.

astro-ph↗
arXiv2001

Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$

General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion paper. The formulas apply in two overlapping limits: for $\ell\gg 1$ and for $\ell d/d_A\ll 1$ (where $d_A$ is the angular diameter distance of the surface of last scattering, and $d$ is a length, of the order of the acoustic horizon at the time of last scattering, that characterizes acoustic oscillations before this time.) The frequently used approximation that $C_\ell$ receives its main contribution from wave numbers of order $\ell/d_A$ is found to be less accurate for the contribution of the Doppler effect than for the Sachs--Wolfe effect and intrinsic temperature fluctuations. For $\ell d/d_A\ll 1$ and $\ell\geq 2$, the growth of $C_\ell$ with $\ell$ is shown to be affected by acoustic oscillation wave numbers of all scales. The asymptotic formulas are applied to a model of acoustic oscillations before the time of last scattering, with results in reasonable agreement with more elaborate computer calculations.

astro-ph↗
arXiv2001

Conference Summary - 20th Texas Symposium on Relativistic Astrophysics

This is the written version of the summary talk given at the 20th Texas Symposium on Relativistic Astrophysics in Austin, Texas, on December 15, 2000. After a brief summary of some of the highlights at the conference, comments are offered on three special topics: theories with large additional spatial dimensions, the cosmological constant problems, and the analysis of fluctuations in the cosmic microwave background.

astro-ph↗
arXiv2000

Curvature Dependence of Peaks in the Cosmic Microwave Background Distribution

The widely cited formula $\ell_1\simeq 200 Ω_0^{-1/2}$ for the multipole number of the first Doppler peak is not even a crude approximation in the case of greatest current interest, in which the cosmic mass density is less than the vacuum energy density. For instance, with $Ω_M$ fixed at 0.3, the position of any Doppler peak varies as $Ω_0^{-1.58}$ near $Ω_0=1$.

astro-ph↗
arXiv2000

The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000)

The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.

astro-ph↗
arXiv2000

A Priori Probability Distribution of the Cosmological Constant

In calculations of the probability distribution for the cosmological constant, it has been previously assumed that the a priori probability distribution is essentially constant in the very narrow range that is anthropically allowed. This assumption has recently been challenged. Here we identify large classes of theories in which this assumption is justified.

astro-ph↗
arXiv1998

Non-Renormalization Theorems in Non-Renormalizable Theories

A perturbative non-renormalization theorem is presented that applies to general supersymmetric theories, including non-renormalizable theories in which the $\int d^2θ$ integrand is an arbitrary gauge-invariant function $F(Φ,W)$ of the chiral superfields $Φ$ and gauge field-strength superfields $W$, and the $\int d^4θ$-integrand is restricted only by gauge invariance. In the Wilsonian Lagrangian, $F(Φ,W)$ is unrenormalized except for the one-loop renormalization of the gauge coupling parameter, and Fayet-Iliopoulos terms can be renormalized only by one-loop graphs, which cancel if the sum of the U(1) charges of the chiral superfields vanishes. One consequence of this theorem is that in non-renormalizable as well as renormalizable theories, in the absence of Fayet-Iliopoulos terms supersymmetry will be unbroken to all orders if the bare superpotential has a stationary point.

hep-th↗
arXiv1997

Effective Field Theories in the Large $N$ Limit

Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the non-linear O(N) $σ$-model, and the $CP^{N-1}$ model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete cancellation of infinities. These models provide qualitative predictions of the form of scattering amplitudes for arbitrary momenta, but because of the infinite number of free parameters, it is possible to derive quantitative predictions only in the limit of small momenta. For small momenta the large-$N$ limit provides only a modest simplification, removing at most a finite number of diagrams to each order in momenta, except near phase transitions, where it reduces the infinite number of diagrams that contribute for low momenta to a finite number.

hep-th↗
arXiv1997

Likely Values of the Cosmological Constant

In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this ``collapsed fraction'' by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density fluctuations in a flat universe with arbitrary value of the cosmological constant, applied in a statistical way to the observed spectrum of density fluctuations at recombination. From this, the probability distribution for the vacuum energy density rho_V=Lambda/8pi G for Gaussian random density fluctuations is derived analytically. It is shown that the results depend on only one quantity, sigma^3 RHO, where sigma^2 and RHO are the variance and mean value of the fluctuating matter density field at recombination, respectively. To calculate sigma, we adopt the flat CDM model with nonzero cosmological constant and fix the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of rho_V with present observational bounds on the cosmological constant indicates that the small, positive value of rho_V (up to 3 times greater than the present cosmic mass density) suggested recently by several lines of evidence is a reasonably likely value to observe, even if all values of rho_V are equally likely a priori.

astro-ph↗
arXiv1996

Theories of the Cosmological Constant

This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how to calculate the probability distribution of the observed cosmological constant in cosmological theories with a large number of subuniverses (i. e., different expanding regions, or different terms in the wave function of the universe) in which this constant takes different values.

astro-ph↗
arXiv1996

Are Nonrenormalizable Gauge Theories Renormalizable?

We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the {\em a priori} constraints that we impose on the form of the bare action correspond to the cohomology of the BRST transformations generated by the action. Recent cohomology theorems of Barnich, Brandt, and Henneaux are used to show that conventionally nonrenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.

hep-th↗
arXiv1994

Strong Interactions at Low Energy

This is a revised version of a talk given at the Chiral Dynamics Workshop at M.I.T., July 25, 1994. It reports results in three areas: (1) The isospin-violating interactions between one non-relativistic nucleon and any number of soft pions can be summarized in a single term in the effective chiral Lagrangian, with no unknown parameters. (2) With D'Hoker, it has been shown that the terms in the Lagrangian for an effective field theory with symmetry $G$ spontaneously broken to $H$, that are not the integrals of $G$-invariant Lagrangian densities, are in one-to-one correspondence with the generators of $H_5(G/H,R)$. (3) If we assume that the nucleon is connected by successive one-pion transitions only to a tower of narrow baryon states with $T=J=1/2,3/2,\dots,N_c/2$, then the Adler-Weisberger and superconvergence relations tell us (for any $N_c$) that (a) the tower states are degenerate, and (b) the one-pion transition amplitudes between these states generate the {\em uncontracted} algebra of $SU(4)\times O(3)$.

hep-ph↗
arXiv1994

General Effective Actions

We investigate the structure of the most general actions with symmetry group $G$, spontaneously broken down to a subgroup $H$. We show that the only possible terms in the Lagrangian density that, although not $G$-invariant, yield $G$-invariant terms in the action, are in one to one correspondence with the generators of the fifth cohomology classes. For the special case of $G=SU(N)_L \times SU(N)_R$ broken down to the diagonal subgroup $H=SU(N)_V$, there is just one such term for $N\geq 3$, which for $N=3$ is the original Wess-Zumino-Witten term.

hep-ph↗
arXiv1993

Effective Action and Renormalization Group Flow of Anisotropic Superconductors

We calculate the effective action of a superconductor, without assuming that either the electron-electron potential or the Fermi surface obey rotational invariance. This approach leads to the same gap equation and equilibrium free energy as more conventional methods. The results are used to obtain the Gell-Mann - Low renormalization group equations for the electron-electron potential.

cond-mat↗
arXiv1993

Flavor Changing Scalar Interactions

The smallness of fermion masses and mixing angles has recently been been attributed to approximate global $U(1)$ symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features.

hep-ph↗
arXiv1992

Conference Summary

Talk presented at the XXVI International Conference on High Energy Physics, Dallas, Texas, August, 12, 1992.

hep-ph↗