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Dark Energy with Phantom Crossing and the $H_0$ tension
Eleonora Di Valentino, Ankan Mukherjee, Anjan A. Sen
TL;DR
The paper asks whether phantom crossing in dark energy can address the Hubble tension between early- and late-universe observations. It uses a phenomenological density expansion constrained with combined cosmological datasets, finding evidence for crossing and reduced tension in the full-data fit.
Problem
The paper investigates whether dark energy can undergo phantom crossing and help resolve the discrepancy between local and CMB-based Hubble measurements.
Method
The authors phenomenologically Taylor-expand dark energy density around an extremum and constrain its parameters with combined CMB, H_0, BAO, supernova, and lensing data.
Results
The full dataset gives H_0 = 70.25±0.78 km/s/Mpc, with phantom crossing observed at more than 2σ and improved χ2 relative to ΛCDM.
Takeaways & Limitations
Phantom crossing substantially alleviates the Hubble tension while remaining consistent across the different dataset combinations.
Takeaways & Limitations
The reconstruction assumes spatial flatness, independently conserved matter, dark energy, and radiation, and allows dark energy density to become negative.
Abstract
from arXiv · showhide
We investigate the possibility of phantom crossing in the dark energy sector and solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the CMB, local measurement of Hubble constant ($H_0$), BAO and SnIa for this purpose. For a combination of CMB+BAO data which is related to early Universe physics, phantom crossing in the dark energy sector is confirmed at $95$\% confidence level and we obtain the constraint $H_0=71.0^{+2.9}_{-3.8}$ km/s/Mpc at 68\% confidence level which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combination of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtain the constraint $H_0=70.25\pm 0.78$ km/s/Mpc at 68\% confidence level and the phantom crossing happening at the scale factor $a_m=0.851^{+0.048}_{-0.031}$ at 68\% confidence level.
1. INTRODUCTION
The paper examines whether dark energy can cross the phantom divide and whether this behavior can address the discrepancy between local and CMB-based Hubble measurements.
- 1. INTRODUCTION: Phantom crossing is tested as a possible explanation for the disagreement between local and CMB-inferred Hubble parameters.
- 1. INTRODUCTION: Dark energy is classified as phantom for w_DE < −1 and non-phantom for w_DE > −1, with w_DE = −1 marking the phantom barrier.
- 1. INTRODUCTION: The local measurement gives H_0 = 74.03±1.42 km/s/Mpc, while Planck’s ΛCDM estimate is H_0 = 67.27 ± 0.60 km/s/Mpc, producing a 4.4σ tension.
- 1. INTRODUCTION: The reconstruction is phenomenological, assumes a phantom crossing without specifying dark energy’s physical entity, and constrains a truncated density expansion statistically.
2. RECONSTRUCTION OF THE MODEL
The model parametrizes dark energy through its density, expanding around an extremum that represents phantom crossing and restricting the expansion to third order.
- 2. RECONSTRUCTION OF THE MODEL: Using ρ_DE rather than w_DE gives a simpler, more direct contribution to H(z), avoiding the redshift integration required for w_DE.
- 2. RECONSTRUCTION OF THE MODEL: The dark energy density is Taylor-expanded around an extremum at a_m, where its derivative changes sign and phantom crossing can occur.
- 2. RECONSTRUCTION OF THE MODEL: The parametrization is ρ_DE(a) = ρ_0[1 + α(a − a_m)^2 + β(a − a_m)^3], with the first-order term omitted at the extremum.
- 2. RECONSTRUCTION OF THE MODEL: The expansion is truncated at third order because higher-order terms would introduce parameters that current data may not tightly constrain.
- 2. RECONSTRUCTION OF THE MODEL: At early times, the resulting equation of state approaches w_DE → −1, giving cosmological-constant behavior without a convergence issue.
- 2. RECONSTRUCTION OF THE MODEL: The model reduces to ΛCDM when α = β = 0, and a_m < 1 signals a transition before the present day.
3. METHODOLOGY
The analysis combines CMB, local Hubble, BAO, supernova, and lensing observations to constrain a nine-parameter cosmological model using Monte Carlo sampling.
- 3. METHODOLOGY: The dataset suite includes Planck CMB spectra, the SH0ES H_0 prior, BAO, Pantheon supernovae, and CMB lensing reconstruction.
- 3. METHODOLOGY: The baseline varies nine parameters: standard cosmological quantities plus α, β, and a_m describing the dark energy density expansion.
- 3. METHODOLOGY: The dark energy parameters are constrained with flat uniform priors and posterior sampling using a modified CosmoMC implementation.
4. OBSERVATIONAL CONSTRAINTS
Across dataset combinations, the phantom-crossing model raises the inferred Hubble constant and provides evidence for a dark-energy transition, while fitting the expansion-rate data well.
- CMB alone leaves am bimodal, whereas adding BAO, Pantheon, or R19 selects the other posterior peak than CMB+lensing.Additional probes are therefore needed to distinguish the preferred value of am.
- Phantom Crossing improves the Δχ2 relative to ΛCDM for every dataset combination considered, including BAO alone.The paper also reports a significant improvement in the total Δχ2 for the joint analysis.
- H0 = 71.0+2.9−3.8 km/s/Mpc at 68% CL for CMB+BAO, consistent with the R19 local measurement.The CMB+BAO fit also indicates am = 0.859 ± 0.064, α = 7.3 ± 3.9, and β = 16.1 ± 7.8.
- The H0 increase is associated with positive correlations with α and β and, for CMB+BAO, a negative correlation with am.For CMB+Pantheon, H0 is instead positively correlated with am; the preferred larger H0 persists across combinations.
- The joint constraints give am = 0.851+0.048−0.047, with a dark-energy transition favored at more than 2σ.The present-day equation of state is wDE(z = 0) = −1.33+0.31−0.42 at 95% CL, ruling out the cosmological constant at more than 2σ.
- The constrained model can keep the Planck-inferred sound horizon rd while agreeing with BAO and a larger H0, possibly through non-monotonic late-time dark-energy evolution.The authors also note that ρDE(z) may become negative at some redshifts, which may help reduce the Hubble tension.
5. CONCLUSION
The study tests a phenomenological phantom-crossing dark-energy model against Planck and other cosmological observations. The combined data constrain H0 to 70.25 ± 0.78 km/s/Mpc, support crossing before the present epoch, and show improved fit relative to ΛCDM.
- H0 = 70.25 ± 0.78 km/s/Mpc at 68% CL for the full dataset, reducing the tension with R19 to 2.3 standard deviations.
- The full dataset indicates phantom crossing at more than 2σ, with the transition occurring at a scale factor below one.A scale factor am < 1 places the crossing before the present day.
- The Phantom Crossing model fits the full dataset better than ΛCDM according to the reported χ2 comparison.