We study the effects of long wavelength entropy fluctuations on cosmological probes such as galaxy clustering, luminosity distance, and CMB temperature anisotropies. Specifically, we consider fluctuations of a massless spectator scalar field set up in the early universe, which later acquires mass during the radiation-dominated era. We find that there are non-vanishing effects on observables, and the amplitude of these effects peaks for observables set up at the time of equal matter and radiation, and decreases as $\eta^{ -2}$ where $\eta$ is the conformal time. Hence, the back-reaction effects are important for CMB anisotropies, but their impact on late-time observables is suppressed. In particular, the back-reaction effects are unable to explain the Hubble tension while they might alleviate the cosmic dipole tension. In contrast to a lot of the previous work on back-reaction, we work in position rather than momentum space.
Categories: astro-ph.CO gr-qc hep-ph hep-th