How do I install rails and create a new application without root access?

I am trying to install Ruby on Rails on a Linux machine in my home directory (without root access). My ruby version is ruby 2.1.5p273 (2014-11-13) [x86_64-linux-gnu]. So far I was able to:

$ gem install --user-install rails

which apparently has installed rails into ~/.gem/ruby/2.1.0/bin/rails:

$ ./.gem/ruby/2.1.0/bin/rails --version
Rails 4.2.6

But then it fails to create the application:

$ ~/.gem/ruby/2.1.0/bin/rails new myapp
  create  
  create  README.rdoc
  create  Rakefile
  create  config.ru
  create  .gitignore
  create  Gemfile
  create  app
  create  app/assets/javascripts/application.js
  create  app/assets/stylesheets/application.css
  create  app/controllers/application_controller.rb
  create  app/helpers/application_helper.rb
  create  app/views/layouts/application.html.erb
  create  app/assets/images/.keep
  create  app/mailers/.keep
  create  app/models/.keep
  create  app/controllers/concerns/.keep
  create  app/models/concerns/.keep
  create  bin
  create  bin/bundle
  create  bin/rails
  create  bin/rake
  create  bin/setup
  create  config
  create  config/routes.rb
  create  config/application.rb
  create  config/environment.rb
  create  config/secrets.yml
  create  config/environments
  create  config/environments/development.rb
  create  config/environments/production.rb
  create  config/environments/test.rb
  create  config/initializers
  create  config/initializers/assets.rb
  create  config/initializers/backtrace_silencers.rb
  create  config/initializers/cookies_serializer.rb
  create  config/initializers/filter_parameter_logging.rb
  create  config/initializers/inflections.rb
  create  config/initializers/mime_types.rb
  create  config/initializers/session_store.rb
  create  config/initializers/wrap_parameters.rb
  create  config/locales
  create  config/locales/en.yml
  create  config/boot.rb
  create  config/database.yml
  create  db
  create  db/seeds.rb
  create  lib
  create  lib/tasks
  create  lib/tasks/.keep
  create  lib/assets
  create  lib/assets/.keep
  create  log
  create  log/.keep
  create  public
  create  public/404.html
  create  public/422.html
  create  public/500.html
  create  public/favicon.ico
  create  public/robots.txt
  create  test/fixtures
  create  test/fixtures/.keep
  create  test/controllers
  create  test/controllers/.keep
  create  test/mailers
  create  test/mailers/.keep
  create  test/models
  create  test/models/.keep
  create  test/helpers
  create  test/helpers/.keep
  create  test/integration
  create  test/integration/.keep
  create  test/test_helper.rb
  create  tmp/cache
  create  tmp/cache/assets
  create  vendor/assets/javascripts
  create  vendor/assets/javascripts/.keep
  create  vendor/assets/stylesheets
  create  vendor/assets/stylesheets/.keep
     run  bundle install
There was an error while trying to write to `/var/lib/gems/2.1.0`. It is likely that you need to
grant write permissions for that path.
     run  bundle exec spring binstub --all
bundler: command not found: spring
Install missing gem executables with `bundle install`

Does rails require root access??

Thanks!