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    {
      "affiliations": [
        {
          "country": "Portugal", 
          "value": "Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Faculdade de Ci\u00eancias da Universidade de Lisboa, Lisboa, Portugal"
        }
      ], 
      "surname": "Frusciante", 
      "given_names": "Noemi", 
      "full_name": "Frusciante, Noemi"
    }, 
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan"
        }
      ], 
      "surname": "Kase", 
      "given_names": "Ryotaro", 
      "full_name": "Kase, Ryotaro"
    }, 
    {
      "affiliations": [
        {
          "country": "UK", 
          "value": "Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth, United Kingdom"
        }
      ], 
      "surname": "Koyama", 
      "given_names": "Kazuya", 
      "full_name": "Koyama, Kazuya"
    }, 
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan"
        }
      ], 
      "surname": "Tsujikawa", 
      "email": "shinji@rs.kagu.tus.ac.jp", 
      "full_name": "Tsujikawa, Shinji", 
      "given_names": "Shinji"
    }, 
    {
      "affiliations": [
        {
          "country": "Portugal", 
          "value": "Centro de Astrof\u00edsica e Gravita\u00e7\u00e3o \u2013 CENTRA, Departamento de F\u00edsica, Instituto Superior T\u00e9cnico \u2013 IST, Universidade de Lisboa \u2013 UL, Lisboa, Portugal"
        }
      ], 
      "surname": "Vernieri", 
      "given_names": "Daniele", 
      "full_name": "Vernieri, Daniele"
    }
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  "titles": [
    {
      "source": "Elsevier", 
      "title": "Tracker and scaling solutions in DHOST theories"
    }
  ], 
  "dois": [
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      "value": "10.1016/j.physletb.2019.01.009"
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      "journal_title": "Physics Letters B", 
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      "year": 2019, 
      "page_start": "167"
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      "url": "http://creativecommons.org/licenses/by/3.0/", 
      "license": "CC-BY-3.0"
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    {
      "holder": "The Author(s)", 
      "statement": "The Author(s)", 
      "year": "2019"
    }
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  "control_number": "45221", 
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  "abstracts": [
    {
      "source": "Elsevier", 
      "value": "In quadratic-order degenerate higher-order scalar\u2013tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by <math><mover><mrow><mi>\u03d5</mi></mrow><mrow><mo>\u02d9</mo></mrow></mover><mo>/</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>=</mo><mrow><mi>constant</mi></mrow></math>, where <math><mover><mrow><mi>\u03d5</mi></mrow><mrow><mo>\u02d9</mo></mrow></mover></math> is the time derivative of a scalar field \u03d5, H is the Hubble expansion rate, and p is a constant. While the tracker is present up to the cubic-order Horndeski Lagrangian <math><mi>L</mi><mo>=</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>X</mi><mo>\u2212</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msub><msup><mrow><mi>X</mi></mrow><mrow><mo>(</mo><mi>p</mi><mo>\u2212</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>p</mi><mo>)</mo></mrow></msup><mo>\u25a1</mo><mi>\u03d5</mi></math>, where <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msub></math> are constants and X is the kinetic energy of \u03d5, the DHOST interaction breaks this structure for <math><mi>p</mi><mo>\u2260</mo><mn>1</mn></math>. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state <math><msub><mrow><mi>w</mi></mrow><mrow><mi>\u03d5</mi></mrow></msub><mo>=</mo><mo>\u2212</mo><mn>1</mn><mo>\u2212</mo><mn>2</mn><mi>p</mi><mover><mrow><mi>H</mi></mrow><mrow><mo>\u02d9</mo></mrow></mover><mo>/</mo><mo>(</mo><mn>3</mn><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math>. The scaling solution, which corresponds to <math><mi>p</mi><mo>=</mo><mn>1</mn></math>, is the unique case in which all the terms in the field density <math><msub><mrow><mi>\u03c1</mi></mrow><mrow><mi>\u03d5</mi></mrow></msub></math> and the pressure <math><msub><mrow><mi>P</mi></mrow><mrow><mi>\u03d5</mi></mrow></msub></math> obey the scaling relation <math><msub><mrow><mi>\u03c1</mi></mrow><mrow><mi>\u03d5</mi></mrow></msub><mo>\u221d</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>\u03d5</mi></mrow></msub><mo>\u221d</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. Extending the analysis to the coupled DHOST theories with the field-dependent coupling <math><mi>Q</mi><mo>(</mo><mi>\u03d5</mi><mo>)</mo></math> between the scalar field and matter, we show that the scaling solution exists for <math><mi>Q</mi><mo>(</mo><mi>\u03d5</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>/</mo><mo>(</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>\u03d5</mi><mo>+</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math>, where <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>2</mn></mrow></msub></math> are constants. For the constant Q, i.e., <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math>, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of late-time cosmic acceleration preceded by the scaling \u03d5-matter-dominated epoch."
    }
  ], 
  "imprints": [
    {
      "date": "2019-01-17", 
      "publisher": "Elsevier"
    }
  ]
}