The Astrophysical Journal, 885:137 (7pp), 2019 November 10 https://doi.org/10.3847/1538-4357/ab4a0e © 2019. The American Astronomical Society. All rights reserved. A New Measurement of the Hubble Constant and Matter Content of the Universe Using Extragalactic Background Light γ-Ray Attenuation A. Domínguez1 , R. Wojtak2 , J. Finke3 , M. Ajello4 , K. Helgason5 , F. Prada6, A. Desai4 , V. Paliya7 , L. Marcotulli4 , and D. H. Hartmann4 1 IPARCOS and Department of EMFTEL, Universidad Complutense de Madrid, E-28040 Madrid, Spain; [email protected] 2 DARK, Niels Bohr Institute, University of Copenhagen, Lyngbyvej 2, DK-2100 Copenhagen, Denmark; [email protected] 3 U.S. Naval Research Laboratory, Code 7653, 4555 Overlook Avenue SW, Washington, DC 20375-5352, USA 4 Department of Physics and Astronomy, Clemson University, Kinard Lab of Physics, Clemson, SC 29634-0978, USA 5 Science Institute, University of Iceland, IS-107 Reykjavik, Iceland 6 Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, E-18080 Granada, Spain 7 Deutsches Elektronen-Synchrotron, D-15738 Zeuthen, Germany Received 2019 March 28; revised 2019 September 24; accepted 2019 September 28; published 2019 November 8 Abstract The Hubble constant H0 and matter density Ωm of the universe are measured using the latest γ-ray attenuation results from Fermi-LAT and Cerenkov telescopes. This methodology is based upon the fact that the extragalactic background light supplies opacity for very high energy photons via photon–photon interaction. The amount of γ-ray attenuation along the line of sight depends on the expansion rate and matter content of the universe. This +6.0 −1 −1 +0.06 novel strategy results in a value of H0 = 67.4-6.2 km s Mpc and W=m 0.14-0.07. These estimates are independent and complementary to those based on the distance ladder, cosmic microwave background (CMB), clustering with weak lensing, and strong lensing data. We also produce a joint likelihood analysis of our results from γ-rays and those from more mature methodologies, excluding the CMB, yielding a combined value of H0= −1 −1 66.6±1.6 kms Mpc and Ωm=0.29±0.02. Key words: BL Lacertae objects: general – cosmic background radiation – cosmology: observations – diffuse radiation 1. Introduction optical depth measurements at higher energies than Abdollahi et al. (2018), focused in the lower redshift universe. These latter Very high energy photons (VHE, E 30 GeV) travel results are based on blazar observations with Imaging Atmo- impeded through the universe due to the extragalactic spheric Cerenkov telescopes (IACTs). In the present analysis, background light (EBL). The EBL is a diffuse radiation field that fills the universe from ultraviolet through infrared we take advantage of these recent products by comparing them with optical depth estimates based on the EBL models wavelengths, and is mainly produced by star formation ( ) processes over cosmic history (e.g., Hauser & Dwek 2001). developed by Finke et al. 2010 and Domínguez et al. γ (2011). Our methodology allows us to use γ-ray absorption to A -ray and an EBL photon may annihilate and produce an Ω fi electron–positron pair (Nikishov 1962; Gould & Schréder constrain H0 and m simultaneously for the rst time. We 1966). This interaction process generates an attenuation in include an estimate of the systematic uncertainties, including γ those by the EBL models. the spectra of -ray sources above a critical energy. This effect ( ) may be characterized by an optical depth and has been As discussed by Suyu et al. 2012 , multiple paths to γ ( independent determinations of the Hubble constant are needed observed with the current generation of -ray telescopes e.g., ( Ackermann et al. 2012; Abramowski et al. 2013; Domínguez in order to assess and control systematic uncertainties see also Chen & Ratra 2011; Abbott et al. 2017; Freedman et al. 2019; et al. 2013; Biteau & Williams 2015; Domínguez & Ajello ) 2015). The proper density of the absorbing EBL photons along Soares-Santos et al. 2019 . Accurate estimates of H0 provide the line of sight depends on the expansion history and is critical independent constraints on dark energy, spatial curvature, neutrino physics, and general relativity (Freedman therefore cosmology dependent. This fact allowed Domínguez ) & Prada (2013) to measure the local expansion rate of the & Madore 2010; Suyu et al. 2012; Weinberg et al. 2013 . Moreover, independent determinations of the Hubble constant universe, i.e., the Hubble constant H0. Their H0 measurement is based on a comparison between an observational estimate will play a crucial role in resolving the problem of a of the cosmic γ-ray horizon (CGRH;8 Domínguez et al. 2013) discrepancy between the Hubble constant inferred from the ( ) and those derived from an empirical EBL model (Domínguez cosmic microwave background radiation CMB and those ( et al. 2011). from SNe Ia with distance calibration from Cepheids Riess ) Recently, the Fermi-LAT collaboration published an unpre- et al. 2018 . This tension may likely result from currently cedented measurement of the optical depths as a function of unknown systematic effects, but it can also signify an intrinsic Λ ( energy in the redshift range that goes from the local universe inconsistency within the standard CDM e.g., Di Valentino ) to a redshift of approximately 3 (Abdollahi et al. 2018). et al. 2016; Wojtak & Prada 2017 . Ω Furthermore, Desai et al. (2019) have provided complementary Here, we derive a complementary estimate of H0 and m using EBL attenuation data. This paper is organized as follows. 8 The CGRH is defined as the energy at which the EBL absorption optical Section 2 gives theoretical and observational backgrounds, depth is equal to unity as a function of redshift (Fazio & Stecker 1970). whereas Section 3 shows general considerations and describes 1 The Astrophysical Journal, 885:137 (7pp), 2019 November 10 Domínguez et al. our likelihood methodology. In Section 4, we present the two models. First, the physically motivated model by Finke cosmological results. Finally, a discussion and summary of our et al. (2010, hereafter F10, see Section 3.3.1) and second the results is presented in Section 5. observational model by Domínguez et al. (2011, hereafter D11, see Section 3.3.2). According to Abdollahi et al. (2018), 2. Theoretical and Observational Background the F10 model is in excellent agreement with the LAT blazar γ fi The potential of measuring the Hubble constant from γ-ray -ray data, characterized by a signi cance of rejection of the σ attenuation was already pointed out two decades ago by model of only 0.4 . The D11 model is still compatible with the Salamon et al. (1994) and Mannheim et al. (1996), when the data, but was found to have a rejection significance of 2.9σ γ-ray experiments at that time could only study a few sources (which we do not consider significant), mainly due to on the entire sky. Later, Blanch & Martinez (2005a, 2005b, discrepancies at high redshifts. These reported tensions 2005c) studied, in a series of papers, the potential of using the between EBL models and γ-ray observations at high redshift CGRH to constrain cosmology. These investigations were may have some impact on our measurement of Ωm, but we motivated by the starting operation of IACTs such as MAGIC, expect negligible effect on the estimate of the Hubble constant VERITAS, and H.E.S.S. (Lorenz 2004; Weekes et al. 2002; (see Section 4.1 for more details). These two models should Hinton 2004, respectively). Blanch & Martínez used simulated provide a spread of the EBL model systematic uncertainties VHE spectra of blazars, at different redshifts, to estimate how that are consistent with the γ-ray data. Therefore, the some relevant cosmological parameters could be constrained. combination of these two models can provide an estimate of Their analysis was based on the fact that the CGRH depends on the systematic uncertainty introduced in the cosmological the propagation of the VHE photons across large distances, constraints by our uncertainty in the EBL knowledge. When ( ) which is dependent on cosmology. Barrau et al. 2008 derive a combining constraints based on the two EBL models, we > −1 −1 lower limit of the Hubble constant, H0 74 km s Mpc at assume that both models are equally probable. a 68% confidence level, from the observation of γ-ray photons fl Optical depths as a function of energy and redshift are coming from a are of the blazar Mrk 501, which was detected independently derived following both the F10 and D11 by HEGRA (Aharonian et al. 1999). methodology. A 2D grid of values of the Hubble constant As described in Section 3.2, the cosmological dependence of and matter density are fit to the optical depth data using the the optical depth arises both from the cosmic volume ( ) Monte Carlo Markov Chain method for sampling the posterior containing the EBL volume redshift and the distance fl Λ propagated by the gamma-ray in the absorbing medium probability distribution. We assume a at CDM cosmology ( Ω = − Ω ) fi (distance redshift). The knowledge of the EBL has improved which implies, Λ 1 m , well justi ed by all observa- dramatically in the last decade (e.g., Dwek & Krennrich 2013). tions including the CMB. We set the uniform prior that −1 −1 Ω Recently, direct measurements in optical wavelengths of the 40 H0 95 km s Mpc and 0.05 m 0.6 in agree- EBL in the local universe (Matsuoka et al. 2011; Mattila et al. ment with other independent observational constrains. Then, a 2017a, 2017b) have confirmed previous indications (e.g., global fit is performed to the optical depths as a function of Aharonian et al. 2006) of an EBL spectral intensity close to energy in 14 redshift bins, 12 from Abdollahi et al.