Modifying Gravity to Reduce the 𝐻 0 Tension Meng-Xiang Lin, Marco Raveri, Wayne Hu arXiv: 1810.02333 mxlin@uchicago.edu 2018.10.05 at H0 workshop

Motivation Current H0 tension between CMB and local H0 measurements Modified gravity is tested at late times Study modified gravity at early times

Parameterized Phenomenological MG Background: fixed to LCDM Perturbation: 𝑘 2 Φ=−4𝜋𝐺 𝑎 2 𝜌Δ 𝑘 2 Φ−Ψ =12𝜋𝐺 𝑎 2 𝜌+𝑃 𝜎 GR: 𝑘 2 Ψ=−4𝜋𝐺 𝑎 2 𝜇[𝜌Δ+3 𝜌+𝑃 𝜎] 𝑘 2 Φ−𝛾Ψ =12𝜋𝐺 𝑎 2 𝜇 𝜌+𝑃 𝜎 MG: (Hojjati et al. 2011) 𝜇(𝑎,𝑘): the effective strength of gravity (𝐺→𝜇𝐺) 𝛾 𝑎,𝑘 : difference between the gravitational effects on non-relativistic and relativistic matter

𝜇 ∞ =1.2: the value at beginning of the Universe 𝝁, 𝜸 in this work: Step function of time 𝑎 𝑇 : transition time (z=30) 𝜇 0 =1: the value today

Late time parameters: 𝝁 𝟎 , 𝜸 𝟎

Late time parameters: 𝝁 𝟎 , 𝜸 𝟎

Late time parameters: 𝝁 𝟎 , 𝜸 𝟎 It’s very hard to reduce the tension by only changing the lensing potential (by only modifying gravity at late times)

Early time parameter: 𝝁 ∞ Mention the axis —— 𝜇 ∞ =1.2 - - GR

Early time parameter: 𝝁 ∞ Mention the axis —— 𝜇 ∞ =1.2 - - GR

Early time parameter: 𝝁 ∞ Peak locations in GR 1: phase shift 2: driving effect 10

ΛCDM with CMBTT results: H 0 =67.26±0.99 km/s/Mpc μ ∞ with CMBTT results: H 0 =67.80±1.27 km/s/Mpc

split 𝐻 0 ≈70 km/s/Mpc

split 𝐻 0 ≈70 km/s/Mpc

μ ∞ with CMBtension results: H 0 =69.35±0.80 km/s/Mpc CMBall: CMBTT+CMBlens+CMBpol CMBtension: CMBall+H0+WL ΛCDM with CMBTT results: H 0 =67.26±0.99 km/s/Mpc μ ∞ with CMBTT results: H 0 =67.80±1.27 km/s/Mpc μ ∞ with CMBtension results: H 0 =69.35±0.80 km/s/Mpc μ ∞ >1 at 98% CL

μ ∞ with CMBtension results: H 0 =69.35±0.80 km/s/Mpc CMBtension: CMBall+H0+WL ALL: CMBtension+BAO+SN μ ∞ with CMBtension results: H 0 =69.35±0.80 km/s/Mpc μ ∞ >1 at 98% CL μ ∞ with ALL results: H 0 =68.57±0.50 km/s/Mpc μ ∞ >1 at 95% CL

Summary Ability to reduce H 0 tension: μ 0 + γ 0 YES NO μ ∞ NO? γ ∞ CMB TT CMB TT+ CMB Lensing CMB Lensing+ CMB polarization CMB polarization+ H0+WL H0+WL+ BAO+SN μ 0 + γ 0 YES NO μ ∞ NO? γ ∞

CMB anisotropy source functions in k-space

Shift on BAO peak

TE residual for 𝜇 ∞

Relation between lensing and 𝜎 8 𝑊𝐿 Ω 𝑚 0.5

Impact on lensing potential