Monopole Fluctuation of the CMB and its Gauge Invariance

Abstract

The standard theoretical description $\Theta (\hat{n})$ of the observed CMB temperature anisotropies is gauge-dependent. It is, however, well known that the gauge mode is limited to the monopole and the higher angular multipoles ${\Theta }_l$ ($l\ge 1$) are gauge-invariant. Several attempts have been made in the past to properly define the monopole fluctuation, but the resulting values of the monopole power $C_0$ are infinite due to the infrared divergences. The infrared divergences arise from the contribution of the uniform gravitational potential to the monopole fluctuation, in violation of the equivalence principle. Here we present the gauge-invariant theoretical description of the observed CMB temperature anisotropies and compute the monopole power $C_0=1.66\times 10^{-9}$ in a $\Lambda$CDM model. While the gauge-dependence in the standard calculations originates from the ambiguity in defining the hypersurface for the background CMB temperature $\bar{T}$ today, it is in fact well defined and one of the fundamental cosmological parameters. We argue that once the cosmological parameters are chosen, the monopole fluctuation can be unambiguously inferred from the angle-average of the observed CMB temperature, making it a model-dependent ''observable''. Adopting simple approximations for the anisotropy formation, we derive a gauge-invariant analytical expression for the observed CMB temperature anisotropies to study the CMB monopole fluctuation and the cancellation of the uniform gravitational potential contributions on large scales.

arXiv comment17 pages, 4 figures, accepted for publication in PRD

References in corpus (29)

• Efficient Computation of CMB anisotropies in closed FRW models
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• The Temperature of the Cosmic Microwave Background
• Detection of Polarization in the Cosmic Microwave Background using DASI
• A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope
• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
• CMB Anisotropies: Total Angular Momentum Method
• The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra
• Large-scale clustering of galaxies in general relativity
• A Complete Treatment of CMB Anisotropies in a FRW Universe
• A Two-Fluid Approximation for Calculating the Cosmic Microwave Background Anisotropies
• Gauging the cosmic microwave background
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• Galaxy Power Spectrum in General Relativity
• Galaxy Two-Point Correlation Function in General Relativity
• Proper-Time Hypersurface of Non-Relativistic Matter Flows: Galaxy Bias in General Relativity
• Non-linear general relativistic effects in the observed redshift
• General and consistent statistics for cosmological observations
• $\bar{T}$: A New Cosmological Parameter?
• The Sachs-Wolfe Effect: Gauge Independence and a General Expression
• Gauge-Invariant Formalism of Cosmological Weak Lensing
• Cosmological Information Contents on the Light-Cone
• Tetrad formalism for exact cosmological observables

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• Large gauge transformations, local coordinates and cosmological observables
• Conditions for the Absence of Infrared Sensitivity in Cosmological Probes in Any Gravity Theories
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Monopole Fluctuations in Galaxy Surveys
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• Cosmic Dipoles from Large-Scale Structure Surveys
• Living in a Non-Flat Universe: Theoretical Formalism
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects