[Paper Review] Reconciling the Tension Between Planck and BICEP2 Through Early Dark Energy

Lixin Xu, Baorong Chang+1 more|arXiv (Cornell University)|Apr 15, 2014

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes that early dark energy—acting as a radiation-like component in the early universe—can reconcile the tension between Planck and BICEP2's measurements of the tensor-to-scalar ratio $r$. By introducing an effective neutrino species from early dark energy, the model reduces the inferred sound horizon at recombination, shifting CMB and BAO distance priors to alleviate the $r$-tension at the 2σ level, while also resolving the Hubble constant tension.

ABSTRACT

We show the possibility that the observational results of the primordial gravitational waves from Planck and BICEP2 for the tensor-to-scalar ratio $r$ can be reconciled when an early dark energy was included. This early dark energy behaves like a radiation component at very early epoch. This is equivalent to induce additional number of effective neutrino species: $ΔN_{eff}=[\frac{7}{8}(\frac{4}{11})^{4/3}]^{-1}ρ_{de}(a)/ρ_γ(a)$, where $ρ_γ(a)$ is the photon energy density and the numerical factors arise from converting to effective neutrino species. And $ρ_{de}(a)$ is the energy density of early dark energy. Combining the Planck temperature data, the WMAP9 polarization data, and the baryon acoustic oscillation data with and without BICEP2 data, we find that in this early dark energy model the tension between the observations from Planck and BICEP2 was relived at $2σ$ regions. But it cannot be removed completely due to the small ratio of early dark energy constrained by the other cosmic observations. As a byproduct, the tension between observed values of Hubble parameter from Planck and the direct measurement of the Hubble constant was removed in this early dark energy model.

Motivation & Objective

• To resolve the significant tension between Planck's upper limit on $r < 0.11$ (95% CL) and BICEP2's measurement of $r = 0.20^{+0.07}_{-0.05}$.
• To investigate whether early dark energy, which behaves like radiation at high redshift, can reconcile these conflicting observations.
• To assess whether such a model can simultaneously alleviate the Hubble constant tension between Planck's inferred $H_0$ and direct measurements.
• To quantify the impact of early dark energy on cosmological parameters using MCMC analysis with Planck, WMAP9, BAO, and BICEP2 data.

Proposed method

• Modeling early dark energy via a parameterized energy density $ ho_{de}(a)$ that mimics radiation at early times and transitions to dark energy at late times, using the form from ref:edeDoran.
• Introducing an effective number of neutrino species via $\Delta N_{\text{eff}} \approx 4.4032 \cdot \Omega_{\text{de}}(a)/\Omega_{\gamma}(a)$, where $\Omega_{\text{de}}(a)$ is the early dark energy density fraction.
• Performing a Markov Chain Monte Carlo (MCMC) analysis on the combined datasets: Planck temperature, WMAP9 polarization, BAO, and BICEP2 B-mode data.
• Comparing constraints on $r$ and $H_0$ in the standard $\Lambda$CDM+$r$ model versus the early dark energy extension.
• Using the Friedmann equation with modified $\Omega_{\text{de}}(a)$ to compute the evolution of the equation of state and its impact on cosmological distances.
• Evaluating the overlap of 68% and 95% credible intervals for $r$ between Planck and BICEP2 to assess tension reduction.

Experimental results

Research questions

• RQ1 Can early dark energy reduce the tension between Planck’s $r < 0.11$ and BICEP2’s $r = 0.20^{+0.07}_{-0.05}$ at the 2σ level?
• RQ2 How does the inclusion of early dark energy affect the inferred sound horizon at recombination and the resulting distance priors?
• RQ3 Does the early dark energy model resolve the Hubble constant tension between Planck’s $H_0 \approx 71.7$ km/s/Mpc and the direct measurement $H_0 = 73.8 \pm 2.4$ km/s/Mpc?
• RQ4 What is the maximum allowed early dark energy fraction consistent with other cosmological observations like CMB and BAO?
• RQ5 Why is the tension not fully removed despite the model’s ability to reduce it?

Key findings

• The inclusion of early dark energy reduces the tension between Planck and BICEP2 on the tensor-to-scalar ratio $r$ to the 2σ level, as evidenced by overlapping 95% credible intervals in the MCMC analysis.
• The best-fit $r$ value for the Planck+W+BICEP2+BAO dataset in the early dark energy model is $r = 0.152_{-0.041}^{+0.032}$, which lies within the 2σ region of BICEP2’s $r = 0.20^{+0.07}_{-0.05}$.
• The model constrains the early dark energy fraction to $\Omega^{e}_{\text{de}} = 0.00495_{-0.00495}^{+0.00107}$, indicating a small but non-zero contribution at early times.
• The Hubble constant tension is resolved: the model yields $H_0 = 71.67_{-3.43}^{+2.58}$ km/s/Mpc (Planck+W+BAO) and $H_0 = 71.38_{-3.38}^{+2.49}$ km/s/Mpc (with BICEP2), both consistent with the direct measurement of $73.8 \pm 2.4$ km/s/Mpc.
• The tension cannot be fully removed because the early dark energy fraction is constrained to be small by other cosmological data, limiting its impact on $r$.
• The effective neutrino species contribution from early dark energy is $\Delta N_{\text{eff}} \approx 4.4032 \cdot \Omega_{\text{de}}(a)/\Omega_{\gamma}(a)$, which modifies the radiation density and thus affects the sound horizon and distance priors.